Constructions of Totally Non-Negative Pfaffian

2026/01/11 by Jen-Hsu Chang · 1 voice
Physics and Astronomy · #nlin.SI

paper · pdf

Abstract

The totally non-negative pfaffian (TNNP) is define for a skew-symmetric matrix such that all the sub-pfaffians are non-negative. It appears in the pfaffian structure of τ-function for the non-singular web solitons of the BKP equation . One constructs TNNP using the Perfect matching, chord diagram and the Dyck paths enumeration.Its tridiagonal form is also investigated.

Citations

• Polynomial tau-functions of BKP and DKP hierarchies
• Multiparameter Schur Q-Functions Are Solutions of the BKP Hierarchy
• A generalization of Kuo condensation
• Pfaffian structures and certain solutions to BKP hierarchies I. Sums over partitions
• Pfaffian decomposition and a Pfaffian analogue of q-Catalan Hankel determinants
• KP solitons in shallow water
• On the Drinfeld-Sokolov Hierarchies of D type
• BKP and CKP revisited: The odd KP system
• A relationship between rational and multi-soliton solutions of the BKP hierarchy
• Applications of Graphical Condensation for Enumerating Matchings and Tilings
• Hypergeometric functions related to Schur Q-polynomials and BKP equation
• Darboux transformation for the modified Veselov-Novikov equation
• Modified Novikov--Veselov equation and differential geometry of surfaces

Discussions

• Jen-Hsu Chang: Constructions of Totally Non-Negative Pfaffian https://arxiv.org/abs/2601.06892 https://arxiv.org/pdf/2601.06892 https://arxiv.org/html/2601.06892 [bsky, 0 points, 0 comments]

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