Constructions of Totally Non-Negative Pfaffian
Jen-Hsu Chang
TL;DR
This paper explores the properties and constructions of the totally non-negative pfaffian, a mathematical object relevant to soliton solutions and combinatorial structures, providing new insights into its structure and forms.
Contribution
It introduces novel methods for constructing TNNP using perfect matchings, chord diagrams, and Dyck paths, and investigates its tridiagonal form.
Findings
TNNP can be constructed via combinatorial methods
The tridiagonal form of TNNP is characterized
Connections to web solitons of the BKP equation are established
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 -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.
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Taxonomy
TopicsNonlinear Waves and Solitons · Polynomial and algebraic computation · Algebraic structures and combinatorial models