Linear bound on extremal functions of some forbidden patterns in 0-1 matrices |
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Authors: | Radoslav Fulek |
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Affiliation: | School of Computing Science, Simon Fraser University, Burnaby, BC, Canada V5A 1S6 |
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Abstract: | In this note by saying that a 0-1 matrix A avoids a pattern P given as a 0-1 matrix we mean that no submatrix of A either equals P or can be transformed into P by replacing some 1 entries with 0 entries. We present a new method for estimating the maximal number of the 1 entries in a matrix that avoids a certain pattern. Applying this method we give a linear bound on the maximal number of the 1 entries in an n by n matrix avoiding pattern L1 and thereby we answer the question that was asked by Gábor Tardos. Furthermore, we use our approach on patterns related to L1. |
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Keywords: | Forbidden submatrices Pattern avoidance Extremal problems Linear bounds |
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