Degrees of nonlinearity in forbidden 0-1 matrix problems

@article{Pettie2011DegreesON,
  title={Degrees of nonlinearity in forbidden 0-1 matrix problems},
  author={Seth Pettie},
  journal={Discrete Mathematics},
  year={2011},
  volume={311},
  pages={2396-2410}
}
A 0-1 matrix A is said to avoid a forbidden 0-1 matrix (or pattern) P if no submatrix of A matches P , where a 0 in P matches either 0 or 1 in A. The theory of forbidden matrices subsumes many extremal problems in combinatorics and graph theory such as bounding the length of Davenport-Schinzel sequences and their generalizations, Stanley and Wilf’s permutation avoidance problem, and Turán-type subgraph avoidance problems. In addition, forbidden matrix theory has proved to be a powerful tool in… CONTINUE READING
Highly Cited
This paper has 23 citations. REVIEW CITATIONS

References

Publications referenced by this paper.
Showing 1-10 of 38 references

The maximum number of unit distances in a convex n-gon

J. Comb. Theory, Ser. A • 1990
View 20 Excerpts
Highly Influenced

Extremal functions of forbidden double permutation matrices

J. Comb. Theory, Ser. A • 2009
View 20 Excerpts
Highly Influenced

On 0-1 matrices and small excluded submatrices

J. Comb. Theory, Ser. A • 2005
View 9 Excerpts
Highly Influenced

Excluded permutation matrices and the Stanley-Wilf conjecture

J. Comb. Theory, Ser. A • 2004
View 7 Excerpts
Highly Influenced

Davenport-Schinzel theory of matrices

Discrete Mathematics • 1992
View 10 Excerpts
Highly Influenced

On linear forbidden submatrices

J. Comb. Theory, Ser. A • 2009
View 18 Excerpts
Highly Influenced

Forbidden paths and cycles in ordered graphs and matrices

J. Pach, G. Tardos
Israel J. Math., 155:359–380 • 2006
View 10 Excerpts
Highly Influenced

An Extremal Problem on Sparse 0-1 Matrices

SIAM J. Discrete Math. • 1991
View 6 Excerpts
Highly Influenced

Generalized Davenport-Schinzel Sequences

Combinatorica • 1994
View 5 Excerpts
Highly Influenced

Similar Papers

Loading similar papers…