More minor summation formulae
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arXiv
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| Main Authors: | , , , , , , , , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911534906605568 |
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| author | Chern, Shane Eisenkölbl, Theresia Fischer, Ilse Gangl, Moritz Gatzweiler, Mona Gutiérrez, Álvaro Krattenthaler, Christian Kumari, Nishu Reibnegger, Markus Schönfelder, Marcus Yoshida, Atsuro |
| author_facet | Chern, Shane Eisenkölbl, Theresia Fischer, Ilse Gangl, Moritz Gatzweiler, Mona Gutiérrez, Álvaro Krattenthaler, Christian Kumari, Nishu Reibnegger, Markus Schönfelder, Marcus Yoshida, Atsuro |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21021 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | More minor summation formulae Chern, Shane Eisenkölbl, Theresia Fischer, Ilse Gangl, Moritz Gatzweiler, Mona Gutiérrez, Álvaro Krattenthaler, Christian Kumari, Nishu Reibnegger, Markus Schönfelder, Marcus Yoshida, Atsuro Combinatorics Primary 15A15, Secondary 05A15 05A19 05B45 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. |
| title | More minor summation formulae |
| topic | Combinatorics Primary 15A15, Secondary 05A15 05A19 05B45 |
| url | https://arxiv.org/abs/2603.21021 |