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

Monday 4
Combinatorics
Karen Yeats
› 17:30 - 19:00 (1h30)
› SFU Harbour Center - Segal Centre Conference Rooms 1400 - 1410
Symmetric matrices, Catalan paths, and correlations
Emmanuel Tsukerman  1  , Lauren Williams  1  , Bernd Sturmfels  2@  
1 : Department of Mathematics, University of California, Berkeley, CA
2 : Berkeley University of California  (UC BERKELEY)  -  Website
University of California, Berkeley Department of Mathematics 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. 


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