The Cullis' determinant as Pfaffian
Combinatorics
2026-05-15 v1
Abstract
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 as the Pfaffian of the matrix obtained from by matrix multiplication and transposition. Relying on this result, we present an efficient polynomial-time algorithm for calculating the Cullis' determinant of given matrix.
Keywords
Cite
@article{arxiv.2605.14010,
title = {The Cullis' determinant as Pfaffian},
author = {Alexander Guterman and Andrey Yurkov},
journal= {arXiv preprint arXiv:2605.14010},
year = {2026}
}