An extremal problem on sparse 0-1 matrices
SIAM Journal on Discrete Mathematics
Davenport-Schnizel theory of matrices
Discrete Mathematics
Excluded permutation matrices and the Stanley-Wilf conjecture
Journal of Combinatorial Theory Series A
On 0-1 matrices and small excluded submatrices
Journal of Combinatorial Theory Series A
Note: On linear forbidden submatrices
Journal of Combinatorial Theory Series A
On nonlinear forbidden 0-1 matrices: a refutation of a Füredi-Hajnal conjecture
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Applications of forbidden 0-1 matrices to search tree and path compression-based data structures
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Generalized Davenport-Schinzel sequences and their 0-1 matrix counterparts
Journal of Combinatorial Theory Series A
On the structure and composition of forbidden sequences, with geometric applications
Proceedings of the twenty-seventh annual symposium on Computational geometry
Origins of Nonlinearity in Davenport-Schinzel Sequences
SIAM Journal on Discrete Mathematics
Tight bounds on the maximum size of a set of permutations with bounded VC-dimension
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Tight bounds on the maximum size of a set of permutations with bounded VC-dimension
Journal of Combinatorial Theory Series A
| Hi-index | 0.00 |
We say a 0-1 matrix A avoids a matrix P if no submatrix of A can be transformed into P by changing some ones to zeroes. We call P an m-tuple permutation matrix if P can be obtained by replacing each column of a permutation matrix with m copies of that column. In this paper, we investigate nxn matrices that avoid P and the maximum number ex(n,P) of ones that they can have. We prove a linear bound on ex(n,P) for any 2-tuple permutation matrix P, resolving a conjecture of Keszegh [B. Keszegh, On linear forbidden matrices, J. Combin. Theory Ser. A 116 (1) (2009) 232-241]. Using this result, we obtain a linear bound on ex(n,P) for any m-tuple permutation matrix P. Additionally, we demonstrate the existence of infinitely many minimal non-linear patterns, resolving another conjecture of Keszegh from the same paper.