More minor summation formulae
Combinatorics
2026-03-24 v1
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.
Cite
@article{arxiv.2603.21021,
title = {More minor summation formulae},
author = {Shane Chern and Theresia Eisenkölbl and Ilse Fischer and Moritz Gangl and Mona Gatzweiler and Álvaro Gutiérrez and Christian Krattenthaler and Nishu Kumari and Markus Reibnegger and Marcus Schönfelder and Atsuro Yoshida},
journal= {arXiv preprint arXiv:2603.21021},
year = {2026}
}
Comments
17 pages, AmS-LaTeX