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- W4293570082 abstract "We show that the permanent of a matrix is a linear combination of determinants of block diagonal matrices which are simple functions of the original matrix. To prove this, we first show a more general identity involving alpha-permanents: for arbitrary complex numbers alpha and beta, we show that the alpha-permanent of any matrix can be expressed as a linear combination of beta-permanents of related matrices. Some other identities for the alpha-permanent of sums and products of matrices are shown, as well as a relationship between the alpha-permanent and general immanants. We conclude with a discussion of the computational complexity of the alpha-permanent and provide some numerical illustrations." @default.
- W4293570082 created "2022-08-30" @default.
- W4293570082 creator A5061917565 @default.
- W4293570082 date "2013-04-03" @default.
- W4293570082 modified "2023-09-28" @default.
- W4293570082 title "Some algebraic identities for the alpha-permanent" @default.
- W4293570082 doi "https://doi.org/10.48550/arxiv.1304.1772" @default.
- W4293570082 hasPublicationYear "2013" @default.
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