Pattern Avoidance in Alternating Sign Matrices |
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Authors: | Robert Johansson Svante Linusson |
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Institution: | (1) Department of Mathematics, KTH-Royal Institute of Technology, SE-100 44 Stockholm, Sweden |
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Abstract: | We generalize the definition of a pattern from permutations to alternating sign matrices. The number of alternating sign matrices
avoiding 132 is proved to be counted by the large Schr?der numbers, 1, 2, 6, 22, 90, 394, .... We give a bijection between
132-avoiding alternating sign matrices and Schr?der paths, which gives a refined enumeration. We also show that the 132-,
123-avoiding alternating sign matrices are counted by every second Fibonacci number.
Received January 2, 2007 |
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Keywords: | 05A15 |
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