## A Combinatorial Object

**Description:** Magic squares are numerical arrays that have
substructures with constant sums. This above design is based on a magic square of order 25, containing the
numbers from 0 to 624. Each row, column, and main diagonal sums to the "magic constant" of 7800.
The numbers in the magic square are represented by a visual base-5 system: four concentric squares
serve as the 1, 5, 25, and 125 places, while shades of grey stand for the numerals 0 to 4.

### more information

About the IPM Combinatorics and Computing Group

Combinatorics is a branch of mathematics that studies finite collections of objects that satisfy certain criteria. Over the past few decades, combinatorics has become an increasingly important part of mathematics. It has strong connections to other areas of mathematics like algebra, number theory and operations research as well as other disciplines such as theoretical computer science, cryptography, information theory, social sciences and biological sciences.

IPM Combinatorics and Computing Group was officially established in 2009 at the School of Mathematics of IPM, although it had been active since the foundation of IPM in 1989. During 1989-2009, the group was directed by G. B. Khosrovshahi, a founding member of IPM. The group plays an important role in carrying out research in combinatorics and computing and related fields in Iran. Researchers from universities across the country collaborate with the group in different capacities: senior researchers, resident researchers, nonresident researchers and students. The group also has some faculty members and postdoctoral research fellows. The researchers of the group have published a lot of papers in top quality international journals. Many renown mathematicians from around world have visited IPM and have had collaborations with the group researchers. The group has organised a number of international conferences covering areas such as graph theory, design theory and computational methods. Weekly seminars on combinatorics and computing is also held since 1992.

The main research areas of the group are:

Algebraic combinatorics
Algebraic graph theory
Computational methods for constructing combinatorial objects
Computational complexity
Cryptography
Flows on graphs and designs
Graph coloring
Quantum computing
Quantum information theory

IPM Combinatorics and Computing Group was officially established in 2009 at the School of Mathematics of IPM, although it had been active since the foundation of IPM in 1989. During 1989-2009, the group was directed by G. B. Khosrovshahi, a founding member of IPM. The group plays an important role in carrying out research in combinatorics and computing and related fields in Iran. Researchers from universities across the country collaborate with the group in different capacities: senior researchers, resident researchers, nonresident researchers and students. The group also has some faculty members and postdoctoral research fellows. The researchers of the group have published a lot of papers in top quality international journals. Many renown mathematicians from around world have visited IPM and have had collaborations with the group researchers. The group has organised a number of international conferences covering areas such as graph theory, design theory and computational methods. Weekly seminars on combinatorics and computing is also held since 1992.

The main research areas of the group are:

Contact Us

**Head of the Group:**Behruz Tayfeh-Rezaie**Email Address:**tayfeh-r at ipm dot ir**Tel:**+98 21 22290928**Fax:**+98 21 22290648**Mailing Address:**School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran