Perfect matchings and the octahedron recurrence

Authors:
David E. Speyer
Affiliations:
Clay Mathematics Institute and University of Michigan, Ann Arbor, USA 48109-1043
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
2007

Citing 5
Cited 3

Alternating-Sign Matrices and Domino Tilings (Part II)

Journal of Algebraic Combinatorics: An International Journal
The Laurent Phenomenon

Advances in Applied Mathematics
Perfect Matchings and Perfect Powers

Journal of Algebraic Combinatorics: An International Journal
Generalized domino-shuffling

Theoretical Computer Science - Special issue: Tilings of the plane
Applications of graphical condensation for enumerating matchings and tilings

Theoretical Computer Science - Combinatorics of the discrete plane and tilings

A periodicity theorem for the octahedron recurrence

Journal of Algebraic Combinatorics: An International Journal
Punctured plane partitions and the q-deformed Knizhnik--Zamolodchikov and Hirota equations

Journal of Combinatorial Theory Series A
Reductions of Young Tableau Bijections

SIAM Journal on Discrete Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

We study a recurrence defined on a three dimensional lattice and prove that its values are Laurent polynomials in the initial conditions with all coefficients equal to one. This recurrence was studied by Propp and by Fomin and Zelivinsky. Fomin and Zelivinsky were able to prove Laurentness and conjectured that the coefficients were 1. Our proof establishes a bijection between the terms of the Laurent polynomial and the perfect matchings of certain graphs, generalizing the theory of Aztec Diamonds. In particular, this shows that the coefficients of this polynomial, and polynomials obtained by specializing its variables, are positive, a conjecture of Fomin and Zelevinsky.