2017/06/03 by Ran Pan, Pan, Ran, Jeffrey B. Remmel +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1706.00993
openalex publication_date 2017/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Goulden and Jackson introduced a very powerful method to study the distributions of certain consecutive patterns in permutations, words, and other combinatorial objects which is now called the cluster method. There are a number of natural classes of combinatorial objects which start with either permutations or words and add additional restrictions. These include up-down permutations, generalized Euler permutations, words with no consecutive repeated letters, Young tableaux, and non-backtracking random walks. We develop an extension of the cluster method which we call the \em generalized cluster method to study the distribution of certain consecutive patterns in such restricted combinatorial objects. In this paper, we focus on block patterns in generalized Euler permutations.