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2020

Pattern-Avoiding (0,1)-Matrices

Brualdi, Richard A., Cao, Lei

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We investigate pattern-avoiding (0,1)-matrices as generalizations of pattern-avoiding permutations.

Our emphasis is on 123-avoiding and 321-avoiding patterns for which we obtain exact results as to the maximum number of 1's such matrices can have.
We also give algorithms when carried out in all possible ways, construct all of the pattern-avoiding matrices of these two types.

Pattern-Avoiding (0,1)-Matrices · Around

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Z. Fűredi and P. Hajnal, Davenport-Schinzel theory of matrices, Discrete Math
1992
Earlier work this paper cites.
A. Marcus and G. Tardos, Excluded pemutation matrices and the Stanley-Wilf conjecture, J. Combin. Theory Ser. A
2004
Earlier work this paper cites.
B. Keszegh, Forbidden submarices in 0-1 matrices, Thesis, Eőtvős Loránd University, 2005
2005
Earlier work this paper cites.

Similar

G. Tardos, On 0-1 matrices and small excluded submatrices, J. Combin. Theory Ser. A
Original
2005
Cited alongside, same era.
R.A. Brualdi, Combinatorial Matrix Classes
2006
Cited alongside, same era.
S. Pettie, Degrees of nonlinearity in forbidden 0-1 matrix problems, Discrete Math
2011
Cited alongside, same era.

Then

S. Pettie, Generalized Davenport-Schinzel sequences and their 0-1 matrix counterparts, J. Combin. Theory Ser. A
2011
Later among the works it cites.
M. Bóna, Combinatorics of Permutations
2012
Later among the works it cites.

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