## A Combinatorial Object

**Notation:** Q_n

**Vertices:** 2^n

**Edges:** 2^{n−1}n

**Diameter:** n

**Girth:** 4 if n ≥ 2

**Chromatic number:** 2

**Spectral Gap:** \frac{2}{n}

**Properties:**

Symmetric, Distance regular, Unit distance, Hamiltonian

### more information

Survey combinatorial articles in the recent issue of the Bulletin of the AMS by Gowers and Spielman, see here.

A set of survey articles on different combinatorial topics, see here.

For the event celebrating Richard Guy's 100th birthday, see here.

Recently, Institute of Combinatorics and Its Applications (ICA) called for nominations for the Euler, Hall, and Kirkman medals plus a new Stanton medal to honor significant lifetime contributions to promoting the discipline of combinatorics. See the call here.

Recently, the journal of "Combinatorics, Physics and their Interactions" has been founded which is dedicated to the new research disipline of combinatorial physics. More info here.

Andrew Suk has determined the correct exponential growth rate for the Erdos-Szekres polygon problem. More info here.

Laszlo Babai claims that he has a quasi-polynomial time algorithm for graph isomorphism problem. More info here.

**Asymptopia**

by Joel Spencer and Laura Florescu

More info here

The First IPM-Isfahan Workshop on Combinatorics, May 20-22, 2014, IPM-Isfahan Branch, Isfahan, Iran.

Peter Keevash announces a proof of the existence conjecture for combinatorial designs, answering a question of Steiner from 1853. Read his preprint

Professor Amin Shokrollahi a former adjunct professor of school of mathematics of IPM received the IEEE Richard W. Hamming Medal together with Dr. Michael Luby, VP of Technology at Qualcomm, "for the conception, development and analysis of practical rateless codes."

**Combinatorics: Ancient&Modern**

Edited by Robin Wilson and John J. Watkins

and Foreword by Ronald Graham

You can read Peter Cameron's blog entry about this book here

Yousef Alavi, a native of Iran, Western Michigan University emeritus in mathematics and statistics, died May 21. He was 85.

**Lander Awarded Inaugural Breakthrough Prize**

Eric S. Lander of the Massachusetts Institute of Technology and Harvard Medical School has been awarded an inaugural 2013 Breakthrough Prize, which carries a cash award of 3,000,000 USD.

**Three Computer Scientists Cited for Innovations that Improve Security**

ACM�s Special Interest Group on Algorithms and Computation Theory (SIGACT) together with the European Association for Theoretical Computer Science (EATCS) will recognize three researchers for their contributions to cryptographic concepts and schemes that provide greater efficiency, flexibility, and security.

**Difference Sets: Connecting Algebra, Combinatorics, and Geometry****Emily H. Moore**

This text is suitable for an undergraduate capstone course, since it illuminates the many links among topics that the students have already studied. To this end, almost every chapter ends with a coda highlighting the main ideas and emphasizing mathematical connections. This book can also be used for self-study by anyone interested in these connections and concrete examples.

An edited version of an interview with John Horton Conway conducted in July 2011 at the first International Mathematical Summer School for Students at Jacobs University, Bremen, Germany, published in Notice May 2013 issue.

More Info"Kenneth Appel, who proved the Four Color Theorem with Wolfgang Haken, died April 19 at the age of 80. Their proof, published in two parts in the Illinois Journal of Mathematics in 1977, was the first major proof that involved extensive computer calculations. The proof earned Appel and Haken the Delbert Ray Fulkerson Prize from the AMS and the Mathematical Programming Society in 1979. "

More Info"On January 25th Dr. Curtis Cooper discovered the 48th known Mersenne prime, 257,885,161-1, a 17,425,170 digit number. This find shatters the previous record prime number of 12,978,189 digits discovered over 4 years ago."

Read more"Alexander Razborov is receiving the 2013 AMS David P. Robbins Prize. The Robbins Prize is given every three years for a paper that reports on novel research in algebra, combinatorics, or discrete mathematics. The prize will be awarded on Thursday, January 10, 2013, at the Joint Mathematics Meetings in San Diego."

Read more**Large Networks and Graph Limits****L�szl� Lov�sz, E�tv�s Lor�nd University, Budapest, Hungary**

Authored by a leading expert in the subject, this coherent and accessible book describes one recent approach to the study of large networks, the limit theory of graphs, which has emerged over the past decade and bears rich connections to other approaches to the study of large networks.

**Recent Trends in Discrete Mathematics**, to be held at TIFR, Mumbai during December 17-20, 2012.

This conference has small number of speakers but included among them are some of the most eminent researchers. Many of the speakers have contributed path-breaking research work, which gave new direction to entire areas of discrete mathematics. Navin Singhi's own research work has strong connections with many of the topics mentioned above. We plan to celebrate Navin Singhi's 64th birthday by exploring these various facets of discrete mathematics.

It has been a sad week for the finite geometry community with the recent news that Dan Hughes passed away on October 22. Dan was an enormous influence on the subject, the people, and the drive of our mathematical community; and his sudden passing is a shock to all of us.

Read more on Peter Cameron's blogRead more on SymOmega

Maria Chudnovsky of Columbia University is named a 2012 MacArthur Fellow for her work on the classifications and properties of graphs.

Daniel Spielman of Yale University is named for his theoretical computer science work on abstract questions that affect the essential aspects of daily life in modern society.

About Chudnovsky

Prof. Ravindra Bapat from Indian Statistical Institute will be visiting the School of Mathematics during June 24 - July 7, 2012. He is invited speaker on 5th Conference on Algebraic Combinatorics and Graph Theory at the University of Kashan (July 3 and 4, 2012).

Lectures of Prof. Ravindra Bapat in IPMEndre Szemer�di receives the 2012 Abel Prize from His Majesty King Harald at the ceremony in Oslo, Norway on May 22. Szemer�di was awarded the Abel Prize "for his fundamental contributions to discrete mathematics and theoretical computer science, and in recognition of the profound and lasting impact of these contributions on additive number theory and ergodic theory."

Endre Szemer�di received the Abel PrizeThe Abel Prize Laureate 2012 International Page

See the video of the ceremony

Mikio Kano, Ibaraki University, Japan.

Read MoreKenta Ozeki, National Institute of Informatics, Japan.

Read MoreThe Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2012 to Endre Szemer�di Alfr�d R�nyi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, and Department of Computer Science, Rutgers, The State University of New Jersey, USA "for his fundamental contributions to discrete mathematics and theoretical computer science, and in recognition of the profound and lasting impact of these contributions on additive number theory and ergodic theory."

The Abel Prize Laureate 2012 International PageHerbert Wilf, founding Editor-in-Chief of The Electronic Journal of Combinatorics, died on January 7, 2012, after a protracted illness. Wilf's contributions to combinatorics have been immense, and through his papers, books, teaching, lectures, and students, he has had a profound influence on the development of combinatorics for nearly fifty years.

Visit Herbert's homepageThe book entitled "The Legend of the King and the Mathematician" is written by Mehdi Behzad and Naghmeh Samini. Penned on demand of the House of Mathematics of Gie�en in Germany, the play discusses mathematical problems in a legendary framework.

Read more (in Persian)There are two conferences on combinatorial optimization in April 2012:

The first is '2nd International Symposium on Combinatorial Optimization' (ISCO 2012), which will be held in Athens, Greece, April 17 - 21, 2012.

The second is '25th Conference of European Chapter on Combinatorial Optimization' (ECCO 2012), which will be held in Antalya, Turkey, April 26 � 28, 2012.

Dr. Reza Naserasr from LRI, Orsay, France, is visiting School of Mathematics of IPM during December 24, 2011 - January 26, 2012.

Visit Reza's homepageGraphs and matrices enjoy a fascinating and mutually beneficial relationship. This interplay has benefited both graph theory and linear algebra. In one direction, knowledge about one of the graphs that can be associated with a matrix can be used to illuminate matrix properties and to get better information about the matrix. Going the other way, linear algebraic properties of one of the matrices associated with a graph can be used to obtain useful combinatorial information about the graph. This book, written by Richard Brualdi, is not a comprehensive study of graphs and matrices. The particular content of the lectures was chosen for its accessibility, beauty, and current relevance, and for the possibility of enticing the audience to want to learn more.

Read moreThe event is celebrated with the publication of a new transcription and translation of Galois� works (edited by Peter M. Neumann) by the European Mathematical Society. �variste Galois (October 25, 1811 - May 31, 1832) was a French mathematician born in Bourg-la-Reine.

Read moreIn honor of Professor Ebadollah Mahmoodian, a one week seminar for students will be held at Sharif University of Technology from October 29 to November 2, 2011. Speakers include: Amir Daneshgar, Hossein Hajiabolhassan, Ebadollah Mahmoodian, Rouzbeh Touserkani and Manouchehr Zaker.

See the seminar posterThe commuting graph of a group is a graph whose vertices are non-central elements of the group and where two distinct vertices are connected by an undirected edge if the corresponding elements commute. In 2006, A. Abdollahi, S. Akbari and H.R. Maimani conjectured that two groups with the same commuting graphs are isomorphic if one of them is a finite non-abelian simple group. Recently, this conjecture was resolved in the affirmative by Ronald Solomon and Andrew Woldar.

Read moreProfessor Drago� Cvetkovi? of University of Belgrade in Serbia will present a mathematics lecture at IPM on October 24, 2011, entitled: "Comments on the Genesis of Spectral Graph Theory".

Read moreProfessor Ivan Gutman of University of Kragujevac in Serbia will present a mathematics lecture at IPM on October 19, 2011, entitled: "Distances in Graphs: Theory and Applications", as a guest speaker for IPM Combinatorics and Computing Group.

Read moreThis conference will be held at Shahid Rajaee Teacher Training University, Tehran, on October 20 - 22, 2011, with the cooperation of IPM Combinatorics and Computing Group. Invited speakers for the conference are: Saeed Akbari, Ali Reza Ashrafi, Drago� Cvetkovi? and Ivan Gutman. The conference will contain sessions focused on algebraic methods and applications to graph theory including Chemical Graph Theory, Graph Spectra, Bioinformatics, QSAR/QSPR Modeling, Group Theory in Chemistry.

Read moreIn honor of Professor Richard Wilson, a conference on combinatorics is organised by Jeff Dinitz, Peter Dukes, Esther Lamken and Qing Xiang on March 25-29, 2012, at California Institute of Technology. Invited speakers for the conference are: Ron Baker, Andries Brouwer, Richard Brualdi, Peter Dukes, Chris Godsil, David Grynkiewicz, Esther Lamken, Po-Shen Loh, Doug Leonard, Alexander Rosa and Doug Stinson.

Read moresThis conference will be held at Bu-Ali Sina University, Hamedan, on November 2-3, 2011, with the cooperation of IPM Combinatorics and Computing Group.

Read more (in Persian)Dr. Shabnam Malik from Forman Christian College University, Lahore, Pakistan, will be guest at IPM during August and September 2011. She will present a mathematics lecture at IPM on September 7, 2011, entitled: "Hamiltonicity in Directed Toeplitz Graphs".

Read moreProfessor Hadi Kharaghani from University of Lethbridge in Canada will be guest at IPM during August 8-21, 2011.

Visit Hadi's homepageThe 2011 Frank Nelson Cole Prize in Number Theory is awarded to Chandrashekhar Khare and Jean-Pierre Wintenberger for their remarkable proof of Serre's modularity conjecture.

Read moreThe Chauvenet Prize is the highest award for mathematical expository writing. It consists of a prize of $1000 and a certificate, and is awarded yearly by the Mathematical Association of America in recognition of an outstanding expository article on a mathematical topic. The prize is named in honor of William Chauvenet and was established through a gift from Julian Coolidge in 1925. Bjorn Poonen of MIT received the Chauvenet Prize in 2011.

Read moreIn a collaborative effort sponsored by the American Institute of Mathematics and the National Science Foundation, a team of mathematicians led by K. Ono developed new techniques to explore the nature of the partition numbers. They proved that partition numbers are 'fractal' for every prime. Accompanying this result was another achievement developing an explicit finite formula for the partition function.

Read moreMath Overflow is an interactive mathematics website, which serves both as a collaborative blog and an online community of mathematicians. It allows users to ask questions, submit answers, and rate both, all while getting brownie points for their activities. It is modeled after *Stack Overflow*, a similar forum for computer programming questions, and uses the *Stack Exchange* software engine.

Professor Daniel Panario of Carleton University in Canada will present a mathematics lecture at IPM on June 20, 2011, entitled: "Polynomials over Finite Fields: Algorithms and Randomness".

Read moreProfessor Hossein Shahmohamad of Rochester Institute of Technology in USA will present a mathematics colloquium at IPM on June 8, 2011, entitled: "Julius Petersen, his graph & its amallamorphs and homeomorphs".

Read moreA workshop on key distribution was held successfully at the school of mathematics in IPM on May 24, 2011. The workshop was focussed on many aspects of key distribution such as key pre-distribution, cover-free families, group testing, separating hash families, perfect hash families, and frame-proof codes.

Read moreThe P=NP question is one of the great problems of science, which has intrigued computer scientists and mathematicians for decades. Despite the abundant research in theoretical computer science regarding the P=NP question, it has not been solved.*The P=NP Question and G�del�s Lost Letter*, written by Richard Lipton, is designed for advanced level students and researchers in computer science, and mathematics as a secondary text and reference book. Computer programmers, software developers and IT professionals working in the related industry of computer science theory, will also find this guide a valuable asset.

These web essays are designed for those who have already discovered the joys of mathematics as well as for those who may be uncomfortable with mathematics. Mathematics is a fast growing and evolving subject. The domain of ways that mathematics is being applied is growing by leaps and bounds. Examples include CT scans, audio CD's, face recognition systems, and cell phone technology. Our goal is to share our excitement about these developments with you.

Read moreJoseph A. Gallian, a mathematics professor at University of Minnesota Duluth, is known for his work toward increasing public understanding an appreciation of mathematics and his undergraduate research program.

Read moreThe Alfr�d R�nyi Institute of Mathematics, the J�nos Bolyai Mathematical Society and the Hungarian Academy of Sciences are organizing a conference to celebrate the 70th birthday of Gyula Katona. The conference will be held on September 3-4, 2011 in Budapest, following EuroComb'11.

Read morePaul Tur�n, one of the greatest Hungarian mathematicians was born 100 years ago, on August 18, 1910. To celebrate this occasion the Alfr�d R�nyi Institute of Mathematics, the J�nos Bolyai Mathematical Society and the Mathematical Institute of E�tv�s Lor�nd University are organizing an international conference devoted to Paul Tur�n's main areas of interest: number theory, selected branches of analysis, and selected branches of combinatorics.

Read moreProfessor Alexandr Kostochka from University of Illinois at Urbana-Champaign, USA, will be guest at IPM during May 14-19, 2011. During his visit, he will give two lectures entitled:

1. List Colorings of Dense Hypergraphs;

2. K_{s, t} Minors in (s+t)-Chromatic Graphs.

A workshop on Graphs and Algorithms is jointly organized by the School of Mathematics & the School of Computer Science and is scheduled to be held at IPM on June 1-2, 2011. Members of the organizing committee include Saieed Akbari, Gholamreza Khosrovshahi, Mohammad Ali Safari, and Hamid Sarbazi-Azad.

Read moreThe June/July 2010 issue of the Notices of the AMS highlights the subject of combinatorics. Over the last 30 years, combinatorics and finite mathematics have become central to the creation of collaboration graphs, Google search algorithms, random graphs, and internet routing. They also play a vital part in queueing theory and the solutions of coloring problems. To showcase these and other related topics and to stress the inspirational role of combinatorics, the June/July issue contains these key features: "The Giant Component: The Golden Anniversary", by Joel Spencer; "The Mathematical Side of M. C. Escher", by Doris Schattschneider; "Graph Theory in the Information Age", by Fan Chung, and "Hadwiger's Conjecture", by Maria Chudnovsky.

Read moreThe Association for Women in Mathematics (AWM) is a non-profit organization founded in 1971. The purpose of the Association for Women in Mathematics is to encourage women and girls to study and to have active careers in the mathematical sciences, and to promote equal opportunity and the equal treatment of women and girls in the mathematical sciences.

Read moreOn the occasion of the sixtieth birthday of Andries Brouwer, a two day symposium on Algebraic Combinatorics and Graph Theory is organised by Aart Blokhuis and Hans Cuypers on March 3-4, 2011 in Eindhoven. Invited speakers for the symposium are: Peter Cameron, Chris Godsil, Willem Haemers, Jack Koolen and Lex Schrijver.

Read moreRead the report of the symposium here by Peter Cameron.

This Book presents nineteen classroom tested projects complete with student handouts, solutions, and notes to the instructor. Topics range from a first day activity that motivates proofs to applications of discrete mathematics to chemistry, biology, and data storage. Other projects provide: supplementary material on classic topics such as the towers of Hanoi and the Josephus problem, how to use a calculator to explore various course topics, how to employ Cuisenaire rods to examine the Fibonacci numbers and other sequences, and how you can use plastic pipes to create a geodesic dome.

Read moreA workshop on Linear Algebraic Techniques in Combinatorics and Graph Theory was held at Banff International Research Station (BIRS), from January 30 to February 4, 2011. Six Iranian combinatorialists: Saieed Akbari, Hadi Kharaghani, Gholamreza B. Khosrovshahi, Ali Mohammadian, Azhvan Sheikh Ahmady and Behruz Tayfeh-Rezaie attended the workshop.

Read moreThis is a one day seminar on combinatorics, graph theory and related topics which will be held at Isfahan University of Technology on Wednesday, Feruary 23, 2011.

Read moreThis conference will be held at University of Isfahan, February 24-25, 2011, with the cooperation of IPM Combinatorics and Computing Group.

Read more (in Persian)This volume contains a collection of papers presented at the international conference IPM 20--Combinatorics 2009, which was held at IPM, May 15-21, 2009.

Read moreThe following sildes based on the talks by Peter Erdos at MSCS/UIC should be of interest to our visitors.

New Developments In The Mathematics Of Phylogenetic TreesSome Phylogenetic Mathematics

The Fulkerson Prize for outstanding papers in the area of discrete mathematics is sponsored jointly by the Mathematical Optimization Society and the American Mathematical Society. Beginning in 1979, up to three awards of $750 each will be presented at each (triennial) International Symposium on Mathematical Programming; they will be paid out of a memorial fund administered by the American Mathematical Society that was established by friends of the late Delbert Ray Fulkerson to encourage mathematical excellence in the fields of research exemplified by his work. Beginning in 1994, the amount of each award is $1,500.

Read moreRead the related article here from AMS Notices, Vol. 57, No. 11, December 2010.

The new Journal of Combinatorics is published by International Press and the Editors-in-Chief are Fan Chung and Ron Graham.

For more information click hereMikio Kano (Ibaraki University, Japan)

Spanning Trees of Graphs

Discrete Mathematics with Colored Objects

In memoriam Ralph Gordon Stanton (1923-2010)

The President of the International Mathematical Union does not have the opportunity to give a 'Presidential Address' during his 4 year tenure. It is not an especially visible or influential position. Our main role is simply to organize the next International Congress. So the decision of the Deutsche Mathematiker Vereinigung to publish a series of ICM-Specials is a welcome opportunity for me to express some of my strongly felt convictions about present trends in Mathematics. Having recently enjoyed my 60th birthday, I am also giving in to the universal biological urge to reflect on a lifetime of involvement with mathematics and make sweeping generalizations which can happily be ignored by younger generations.

Read full article about Trends in the Profession of MathematicsThe Future Impact of Internet-Based Technologies on Academic" Abridged version of an address by Terence Tao given at a meeting of the American Academy of Arts and Sciences, on the occasion of his induction into the Academy, October 10, 2009.

Read full article here