


Linear preservers for the qpermanent, cycle qpermanent expansions, and positive crossings in digraphs
(Preprint)

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Type:

Preprint

National /International:

International

Title: 
Linear preservers for the qpermanent, cycle qpermanent expansions, and positive crossings in digraphs

Publication Date:

20180321

Authors:

 Eduardo Marques de Sá

Abstract:

The qpermanent linear preservers are described. We give several expansion formulas for the qpermanent of a square matrix, based on the cycle factorization of permutations. Some of these formulas are valid for all matrices, but others are not; for each such formula Φ we determine all digraphs D such that Φ holds for all matrices with digraph D. Proof techniques are based on combinatorial results, relating the length (number of inversions) of a permutation, the lengths of its cycles, and a delicate counting of crossings, jumps, and arcunderarc relations in digraphs. We get new algebraic characterizations of noncrossing [acyclic] graphs.

Institution:

DMUC 1809

Online version:

http://www.mat.uc.pt...prints/eng_2018.html

Download:

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