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- W2034380314 abstract "We define involutively self-dual matroids and prove that an enumerator for their bases is the square of a related enumerator for their self-dual bases. This leads to a new proof of Tutte's theorem that the number of spanning trees of a central reflex is a perfect square, and it solves a problem posed by Kalai about higher dimensional spanning trees in simplicial complexes. We also give a weighted version of the latter result. We give an algebraic analogue relating to the critical group of a graph, a finite abelian group whose order is the number of spanning trees of the graph. We prove that the critical group of a central reflex is a direct sum of two copies of an abelian group, and conclude with an analogous result in Kalai's setting." @default.
- W2034380314 created "2016-06-24" @default.
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- W2034380314 date "2009-02-01" @default.
- W2034380314 modified "2023-09-27" @default.
- W2034380314 title "Enumerating bases of self-dual matroids" @default.
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- W2034380314 doi "https://doi.org/10.1016/j.jcta.2008.06.007" @default.
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