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- W3118388618 abstract "The determinants of ${pm 1}$-matrices are calculated by via the oriented hypergraphic Laplacian and summing over an incidence generalization of vertex cycle-covers. These cycle-covers are signed and partitioned into families based on their hyperedge containment. Every non-edge-monic family is shown to contribute a net value of $0$ to the Laplacian, while each edge-monic family is shown to sum to the absolute value of the determinant of the original incidence matrix. Simple symmetries are identified as well as their relationship to Hadamard's maximum determinant problem. Finally, the entries of the incidence matrix are reclaimed using only the signs of an adjacency-minimal set of cycle-covers from an edge-monic family." @default.
- W3118388618 created "2021-01-18" @default.
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- W3118388618 date "2021-01-14" @default.
- W3118388618 modified "2023-09-27" @default.
- W3118388618 title "The Determinant of ${pm 1}$-Matrices and Oriented Hypergraphs" @default.
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