Truncated determinants and the refined enumeration of Alternating Sign Matrices and Descending Plane Partitions
Philippe Di Francesco
TL;DR
This paper discusses advanced combinatorial enumeration techniques involving truncated determinants to refine the counting of Alternating Sign Matrices and Descending Plane Partitions, connecting algebraic combinatorics with statistical physics.
Contribution
It introduces new methods using truncated determinants for more precise enumeration of Alternating Sign Matrices and Descending Plane Partitions.
Findings
Refined enumeration formulas for Alternating Sign Matrices.
New connections between algebraic combinatorics and statistical physics.
Enhanced understanding of combinatorial structures through determinant techniques.
Abstract
Lecture notes for the proceedings of the workshop "Algebraic Combinatorics related to Young diagram and statistical physics", Aug. 6-10 2012, I.I.A.S., Nara, Japan.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Random Matrices and Applications · Algebraic structures and combinatorial models