Extremal functions of excluded tensor products of permutation matrices

Extremal functions of excluded tensor products of permutation matrices

For a 0–1 matrix Q, ex(n,Q) is the maximum number of 1s in an n×n 0–1 matrix of which no submatrix majorizes Q. We show that if P is a permutation matrix and Q is arbitrary, then the order of growth of ex(n,P⊗Q) is almost the same as that of ex(n,Q), extending a result used in Marcus and Tardos’s pr...

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Veröffentlicht in:Discrete mathematics 2012-05, Vol.312 (10), p.1646-1649
1. Verfasser: Hesterberg, Adam
Format: Artikel
Sprache:eng
Schlagworte:
Extremal problem
Forbidden submatrix
Mathematical analysis
Matrices
Matrix methods
Pattern avoidance
Permutations
Proving
Tensors
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Zusammenfassung:For a 0–1 matrix Q, ex(n,Q) is the maximum number of 1s in an n×n 0–1 matrix of which no submatrix majorizes Q. We show that if P is a permutation matrix and Q is arbitrary, then the order of growth of ex(n,P⊗Q) is almost the same as that of ex(n,Q), extending a result used in Marcus and Tardos’s proof of the Stanley–Wilf conjecture.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2012.02.015