publication . Article . Preprint . 2018

Matching fields and lattice points of simplices

Loho, Georg; Smith, Ben;
Open Access
  • Published: 04 Oct 2018
Abstract
We show that the Chow covectors of a linkage matching field define a bijection between certain degree vectors and lattice points, and we demonstrate how one can recover the linkage matching field from this bijection. This resolves two open questions from Sturmfels and Zelevinsky (1993) on linkage matching fields. For this, we give an explicit construction that associates a bipartite incidence graph of an ordered partition of a common set to each lattice point in a dilated simplex. Given a triangulation of a product of two simplices encoded by a set of spanning trees on a bipartite node set, we similarly prove that the bijection from left to right degree vectors ...
Subjects
arxiv: Mathematics::Combinatorics
free text keywords: Mathematics - Combinatorics, 05E45, 52B20, 52B40, 14T05
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publication . Article . Preprint . 2018

Matching fields and lattice points of simplices

Loho, Georg; Smith, Ben;