Cycle lemma, parking functions and related multigraphs

Sen Peng Eu*, Tung Shan Fu, Chun Ju Lai


研究成果: 雜誌貢獻期刊論文同行評審


For positive integers a and b, an (a, b̄)-parking function of length n is a sequence (p1, . . ., pn) of nonnegative integers whose weakly increasing order q1 ≤ . . . ≤ qn satisfies the condition qi < a + (i - 1)b. In this paper, we give a new proof of the enumeration formula for (a, b̄)-parking functions by using of the cycle lemma for words, which leads to some enumerative results for the (a, b̄)-parking functions with some restrictions such as symmetric property and periodic property. Based on a bijection between (a, b̄)-parking functions and rooted forests, we enumerate combinatorially the (a, b̄)-parking functions with identical initial terms and symmetric (a, b̄)-parking functions with respect to the middle term. Moreover, we derive the critical group of a multigraph that is closely related to (a, b̄)-parking functions.

頁(從 - 到)345-360
期刊Graphs and Combinatorics
出版狀態已發佈 - 2010

ASJC Scopus subject areas

  • 理論電腦科學
  • 離散數學和組合


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