A Combinatorial Object
Hadamard matrix of order 428
Description: A Hadamard matrix is a square matrix
whose entries are either +1 (white pixels) or -1 (black pixels) and
whose rows are mutually orthogonal. A Hadamard matrix of order 428, the smallest unknown order
of Hadamard matrices before June 2004, was built by Hadi Kharaghani and Behruz Tayfeh-Rezaie.
Since June 2004, the order 668 has been the smallest multiple of 4 for which no Hadamard matrix
is yet known.
It is conjectured that examples of order 4n exist for all n.
Publications

M. Shahsiah (Joint with L. Maherani),
Turan numbers of complete 3-uniform Berge-hypergraphs
Graphs Combin. (to appear)
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Hamid Reza. Daneshpajouh,
On the chromatic number of generalized Kneser hypergraphs
European J. Combin. 81(2019), 150-155
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E. Ghorbani (Joint with M. Andelic and S. K. Simic),
Vertex types in threshold and chain graphs
Discrete Appl. Math. (to appear)
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R. Javadi (Joint with X. Niu and H. Cao),
The spectrum for large sets of $(3,\lambda$)-GDDs of type $g^{u}$
J. Combin. Des. (to appear)
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M. Alishahi,
A generalization of Gale's lemma
J. Graph Theory 88(2018), 337-346
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M. Alishahi,
On the random version of the Erdos matching conjecture
Discrete Appl. Math. (to appear)
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M. R. Oboudi,
Majorization and the spectral radius of starlike trees
J. Comb. Optim. 36(2018), 121-129
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M. R. Oboudi,
Some results on the independence polynomial of unicycle graphs
Discussiones Mathematicae Graph Theory 38(2018), 515-524
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A. Abdollahi (Joint with F. Jafari),
Zero divisor and unit elements with supports of size 4 in group algebras of torsion-free groups
Comm. Algebra (to appear)
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G.R. Omidi,
On a Question of Erdos and Faudree on the size Ramsey Numbers
SIAM J. Discrete Math. (to appear)
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A. Davoodi (Joint with E. Gyori and A. Methuku),
An Erd\H{o}s-Gallai type theorem for uniform hypergraphs
European J. Combin. 69(2018), 159-162
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A. Mohammadian and B. Tayfeh-Rezaie,
Hadamard matrices with few distinct types
Linear Multilinear Algebra (to appear)
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M. R. Oboudi,
On the eigenvalues and spectral radius of starlike trees
Aequat. Math. (2018), DOI: 10.1007/s00010-017-0533-4
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A. Mohammadian and B. Tayfeh-Rezaie,
Star saturation number of random graphs
Discrete Math. 341(2018), 1166-1170
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G. R. Omidi and M. Shahsiah,
Ramsey numbers of 4-uniform loose cycles
Discrete Appl. Math. 230(2017), 112-120
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