2008/06/02 by Po-Yi Huang, Jun Ma, Huang, Po-Yi +3
Computer Science · Mathematics · #05A20 #15A04 #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #math.CO #msc:05A20 #msc:15A04
paper · pdf · doi:10.48550/arxiv.0806.0281
33 pages
arxiv created 2008/06/02 · openalex publication_date 2008/06/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, let Pn;≤ s;kl denote a set of k-flaw preference sets (a1,...,an) with n parking spaces satisfying that 1≤ ai≤ s for any i and a1=l and pn;≤ s;kl=|Pn;≤ s;kl|. We use a combinatorial approach to the enumeration of k-flaw preference sets by their leading terms. The approach relies on bijections between the k-flaw preference sets and labeled rooted forests. Some bijective results between certain sets of k-flaw preference sets of distinct leading terms are also given. We derive some formulas and recurrence relations for the sequences pn;≤ s;kl and give the generating functions for these sequences.