On q-permanent expansions and a theorem on cycle surgery (Preprint)

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Type: Preprint
National /International: International
Title: On q-permanent expansions and a theorem on cycle surgery
Publication Date: 2017-07-05
Authors: - Eduardo Marques de Sá
Abstract: The q-permanent linear preservers are described, and several expansion formulas for the q-permanent of a square matrix are given. 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. The proof technique is based on a combinatorial result where we accurately evaluate what happens to the the number of inversions of a permutation π when one of its cycles if excised from π. In the last section some structural issues are raised concerning the q-permanent expansions previously studied, and some open problems are presented.
Institution: DMUC 17-35
Online version: http://www.mat.uc.pt...prints/eng_2017.html
Download: Not available
 
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