On alternating signed permutations with the maximal number of fixed points

2015/03/21 by Kyoungsuk Park, Park, Kyoungsuk
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Bayesian Methods and Mixture Models #Genome Rearrangement Algorithms #math.CO

paper · pdf · doi:10.48550/arxiv.1503.06279

arxiv created 2015/03/21 · arxiv updated 2015/03/24

Abstract

A conjecture by R. Stanley on a class of alternating permutations, which is proved by R. Chapman and L. Williams states that alternating permutations with the maximal number of fixed points is equidistributed with derangements. We extend this (type A) result to type B: We prove that various classes of alternating signed permutations with the maximal number of fixed points is equidistributed with certain types of derangements (of type B), respectively.

Related

• A conjecture of Stanley on alternating permutations
• Permutations with Extremal number of Fixed Points
• The largest and the smallest fixed points of permutations
• Counting derangements with signed right-to-left minima and excedances
• Derangements and Relative Derangements of Type B