Name
Abstract | ||
|---|---|---|
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 relate this to a statistics problem pioneered by Joe (2006). Correlation matrices are represented by an explicit bijection from the cube to the elliptope. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1016/j.jcta.2016.06.014 | J. Comb. Theory, Ser. A |
Keywords | Field | DocType |
Schröder paths,Catalan paths,Aztec diamond,Correlation,Positive semidefinite matrix,Minors,Principal minors,Tiling,Elliptope | Discrete mathematics,Combinatorics,Bijection,Matrix (mathematics),Aztec diamond,Square matrix,Symmetric matrix,Monomial,Conjecture,Laurent polynomial,Mathematics | Journal |
Volume | Issue | ISSN |
144 | C | 0097-3165 |
Citations | PageRank | References |
0 | 0.34 | 2 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Bernd Sturmfels | 1 | 926 | 136.85 |
| Emmanuel Tsukerman | 2 | 2 | 2.99 |
| Lauren Williams | 3 | 6 | 2.00 |