2005/07/20 by Olivier Guibert, Guibert, Olivier, Sylvain Pelat-Alloin +1
Computer Science · Mathematics · #05Axx #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05Axx #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.math/0507408
25 pages, 7 figures
arxiv created 2005/07/20 · openalex publication_date 2005/07/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a natural, bivariate, generalization of the nonsingular similarity relations considered by T. Fine. We also provide an enumeration formulae and a generating tree for those relations. The latter allow us to give a new bijection between 321-avoiding derangements and Fine sequences. Moreover, we establish that two special cases are in a one-to-one correspondence with subsets of permutations characterized by forbidden subsequences on the symmetrical group. All our results are established using the technique of generating tree, thus giving entirely bijective proofs.