Matthias Beck & Raman Sanyal Combinatorial Reciprocity Theorems A Snapshot of Enumerative Combinatorics from a

Combinatorial Reciprocity Theorems Enumerative Combinatorics with a Polyhedral Angle

Ehrhart theory, modular flow reciprocity, and the Tutte polynomial

Given an oriented graph G, the modular flow polynomial φG(k) counts the number of nowhere-zero Zk-flows of G. We give a description of the modular flow polynomial in terms of (open) Ehrhart polynomials of lattice polytopes. Using Ehrhart–Macdonald reciprocity we give a combinatorial interpretation for the values of φG at negative arguments which answers a question of Beck and Zaslavsky (Adv Mat...

Combinatorial Reciprocity Theorems An Invitation To Enumerative Geometric Combinatorics

simplicial complex, 122, 136,164acyclic orientation, 5, 218affine hull, 52affine projection, 56alcoved polytope, 227alcoved triangulation, 228alcoves, 227Andrews, George, 125anti-isomorphic, 239anti-symmetric, 11antichain, 13, 28, 182antistar, 168Appel, Kenneth, 2, 20arrangement of hyperplanes, 59, 74, 215ascent, 171, 191big, 235<l...

Recent Advances in Algebraic and Enumerative Combinatorics

Algebraic and enumerative combinatorics is concerned with objects that have both a combinatorial and an algebraic interpretation. It is a highly active area of the mathematical sciences, with many connections and applications to other areas, including algebraic geometry, representation theory, topology, mathematical physics and statistical mechanics. Enumerative questions arise in the mathemati...

Grid Graphs, Gorenstein Polytopes, and Domino Stackings

We examine domino tilings of rectangular boards, which are in natural bijection with perfect matchings of grid graphs. This leads to the study of their associated perfect matching polytopes, and we present some of their properties, in particular, when these polytopes are Gorenstein. We also introduce the notion of domino stackings and present some results and several open questions. Our techniq...