Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)

Extended abstracts listed by author > Williams Lauren

Symmetric matrices, Catalan paths, and correlations
Emmanuel Tsukerman  1  , Lauren Williams  1  , Bernd Sturmfels  1@  
1 : Department of Mathematics [Berkeley]  -  Website
Department of Mathematics, University of California, Evans Hall Berkeley, CA 94720, USA -  États-Unis

Kenyon and Pemantle (2014) gave a formula for the entries of a square matrix in terms of connected principal and almost-principal minors. Each entry is an explicit Laurent polynomial whose terms are the weights of domino tilings of a half Aztec diamond. They conjectured an analogue of this parametrization for symmetric matrices, where the Laurent monomials are indexed by Catalan paths. In this paper we prove the Kenyon-Pemantle conjecture, and apply this to a statistics problem pioneered by Joe (2006). Correlation matrices are represented by an explicit bijection from the cube to the elliptope. 

  • Poster
Online user: 1