×

The derangement problem relative to the Mahonian process. (English) Zbl 1019.60095

The aim of the paper is to survey the variety of \(q\)-derangement problems and to investigate a special class of four Mahonian statistics (the term “Mahonian” is used in honour of the mathematician P. A. McMahon) that arise by twisting the Mahonian process to be applied to a \(q\)-derangement problem by a kind of cycle placement rules. The main contribution of the paper is to provide solutions to the four types of considered Mahonian statistics and to discuss and conjecture some other results on some classes of \(q\)-derangement problems in the proposed framework.

MSC:

60K99 Special processes
05A05 Permutations, words, matrices
05A30 \(q\)-calculus and related topics
PDFBibTeX XMLCite
Full Text: DOI EuDML