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- W2772301230 abstract "We first prove a few simple results to illustrate some algebraic combinatorial features of the q -permanent. This is followed by a characterization of a noncrossing permutation in terms of the numbers of inversions of its cycles. Then we use a family of derivative formulas for the q -permanent of a square matrix A to characterize several structures of noncrossing kind. Each such formula f characterizes a set D f of digraphs, in the sense that D ∈ D f iff f is valid for all matrices A with digraph D . In this way we characterize, among others, digraphs with noncrossing permutation subdigraphs, noncrossing graphs, noncrossing forests. We use the derivative formulas to prove two particular cases of a conjecture on the q -monotonicity of the q -permanent of a Hermitian positive definite matrix." @default.
- W2772301230 created "2017-12-22" @default.
- W2772301230 creator A5056259907 @default.
- W2772301230 date "2018-03-01" @default.
- W2772301230 modified "2023-09-29" @default.
- W2772301230 title "Noncrossing partitions, noncrossing graphs, and q-permanental equations" @default.
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- W2772301230 doi "https://doi.org/10.1016/j.laa.2017.11.024" @default.
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