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arXiv · 1805.10239

A principle for converting Lindstr\"om-type lemmas to Stembridge-type theorems, with applications to walks, groves, and alternating flows

Owen Biesel
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Abstract

We prove that Fomin's generalization of Lindstr\"om's lemma for paths on acyclic directed graphs to walks on general directed graphs also generalizes a theorem of Stembridge in the same way. Moreover, we show that whenever a family of operations satisfies a Lindstr\"om-type determinant relation, a related family of operations satisfies a Stembridge-type Pfaffian relation. We give example applications to Kenyon and Wilson's work on groves and to Talaska's work on alternating flows.

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Owen Biesel. 2018-05-25. A principle for converting Lindstr\"om-type lemmas to Stembridge-type theorems, with applications to walks, groves, and alternating flows. https://arxiv.org/abs/1805.10239

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