2000/08/22 by Toufik Mansour, T. Mansour, Mansour, T. +3
Computer Science · Engineering · Mathematics · #05A05 #05A15 #30B70 #42C05 #Advanced Combinatorial Mathematics #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems #math.CO #msc:05A05 #msc:05A15 #msc:30B70 #msc:42C05
paper · pdf · doi:10.48550/arxiv.math/0008173
8 pages
openalex publication_date 2000/08/22 · arxiv created 2001/06/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A permutation is called layered if it consists of the disjoint union of substrings (layers) so that the entries decrease within each layer, and increase between the layers. We find the generating function for the number of permutations on n letters avoiding (1,2,3) and a layered permutation on k letters. In the most interesting case of two layers, the generating function depends only on k and is expressed via Chebyshev polynomials of the second kind.