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On forbidden submatrices.
- Source :
-
Journal of Combinatorial Theory - Series A . May2015, Vol. 132, p1-13. 13p. - Publication Year :
- 2015
-
Abstract
- Given a k × l ( 0 , 1 ) -matrix F , we denote by fs ( m , F ) the largest number for which there is an m × fs ( m , F ) ( 0 , 1 ) -matrix with no repeated columns and no induced submatrix equal to F . A conjecture of Anstee, Frankl, Füredi and Pach states that, regarding F as fixed, fs ( m , F ) = O ( m k ) . The main results of this paper are that for k = 2 , fs ( m , F ) = O ( m 2 + o m ( 1 ) ) and for k ≥ 3 that fs ( m , F ) = O ( m ( 5 / 3 ) k − 1 + o m ( 1 ) ) . [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00973165
- Volume :
- 132
- Database :
- Academic Search Index
- Journal :
- Journal of Combinatorial Theory - Series A
- Publication Type :
- Academic Journal
- Accession number :
- 100981940
- Full Text :
- https://doi.org/10.1016/j.jcta.2014.11.007