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Catalan matroid decompositions of certai...
Pawlowski, Brendan...

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Catalan matroid decompositions of certain positroids by Pawlowski, Brendan ( Author )
Lemonjar Open Access
Australian National University
07-09-2023
A positroid is the matroid of a matrix whose maximal minors are all nonnegative. Given a permutation $w$ in $S_n$, the matroid of a generic $n \times n$ matrix whose non-zero entries in row $i$ lie in columns $w(i)$ through $n+i$ is an example of a positroid. We enumerate the bases of such a positroid as a sum of certain products of Catalan numbers, each term indexed by the $123$-avoiding permutations above $w$ in Bruhat order. We also give a similar sum formula for their Tutte polynomials. These are both avatars of a structural result writing such a positroid as a disjoint union of matroids, each isomorphic to a direct sum of Catalan matroids and a matroid with one basis.
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Article
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29.34 KB
English
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MYR 0.01
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http://arxiv.org/abs/1502.00158
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