More minor summation formulae
Shane Chern, Theresia Eisenk\"olbl, Ilse Fischer, Moritz Gangl, Mona Gatzweiler, \'Alvaro Guti\'errez, Christian Krattenthaler, Nishu Kumari, Markus Reibnegger, Marcus Sch\"onfelder, Atsuro Yoshida

TL;DR
This paper introduces new determinantal-Pfaffian formulas that generalize existing minor summation formulas, with applications to identities involving skew Schur functions.
Contribution
It presents novel determinantal-Pfaffian formulas based on factorization of determinants involving skew-symmetric and rank-1 matrices, extending prior minor summation results.
Findings
Generalized Pfaffian minor summation formulae
Derived a Cauchy-type identity for skew Schur functions
Established factorization formulas for determinants of specific matrix sums
Abstract
We prove determinantal-Pfaffian formulae that simultaneously generalise the Pfaffian minor summation formula of Ishikawa and Wakayama and Byun's recent minor summation formula. These formulae are based on factorisation formulae for the determinant of the sum of a skew-symmetric matrix and a rank-1 matrix. Applications include a Cauchy-type identity for skew Schur functions.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Mathematical Identities · Random Matrices and Applications
