Emmanuel Tsukerman ; Lauren Williams ; Bernd Sturmfels - Symmetric matrices, Catalan paths, and correlations

dmtcs:6337 - Discrete Mathematics & Theoretical Computer Science, April 22, 2020, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) - https://doi.org/10.46298/dmtcs.6337
Symmetric matrices, Catalan paths, and correlationsArticle

Authors: Emmanuel Tsukerman 1; Lauren Williams 1; Bernd Sturmfels 1

  • 1 Department of Mathematics [Berkeley]

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.


Volume: DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)
Published on: April 22, 2020
Imported on: July 4, 2016
Keywords: Combinatorics,[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
Funding:
    Source : OpenAIRE Graph
  • Graduate Research Fellowship Program; Funder: National Science Foundation; Code: 1106400
  • CAREER: Cluster algebras, total positivity, and physical combinatorics; Funder: National Science Foundation; Code: 1049513
  • Algebraic Geometry: Computations and Applications; Funder: National Science Foundation; Code: 1419018

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