More minor summation formulae

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.