The Cullis' determinant as Pfaffian
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913126094471168 |
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| author | Guterman, Alexander Yurkov, Andrey |
| author_facet | Guterman, Alexander Yurkov, Andrey |
| contents | The Cullis' determinant is a generalization of the ordinary determinant for rectangular matrices. It is defined as the alternating sum of maximal minors of given matrix. In this paper we express the Cullis' determinant of a matrix $X$ as the Pfaffian of the matrix obtained from $X$ by matrix multiplication and transposition.
Relying on this result, we present an efficient polynomial-time algorithm for calculating the Cullis' determinant of given matrix. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14010 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Cullis' determinant as Pfaffian Guterman, Alexander Yurkov, Andrey Combinatorics 15A15, 15B99, 15A69 The Cullis' determinant is a generalization of the ordinary determinant for rectangular matrices. It is defined as the alternating sum of maximal minors of given matrix. In this paper we express the Cullis' determinant of a matrix $X$ as the Pfaffian of the matrix obtained from $X$ by matrix multiplication and transposition. Relying on this result, we present an efficient polynomial-time algorithm for calculating the Cullis' determinant of given matrix. |
| title | The Cullis' determinant as Pfaffian |
| topic | Combinatorics 15A15, 15B99, 15A69 |
| url | https://arxiv.org/abs/2605.14010 |