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. |