Abstract
An involution π is said to be τ-ccontain any subsequence having all the same pairwise comparisons as τ. This paper concerns the enumeration of involutions which avoid a set A κ of subsequences increasing both in number and in length at the same time. Let A κ be the set of all the permutations 12π 3.. π κ. of length k. For κ = 3 the only subsequence in A κ is 123 and the 123-avoiding involutions of length n are enumerated by the central binomial coefficients (n/⌊n/2]). For k = 4 we give a combinatorial explanation that shows the number of involutions of length n avoiding A 4 is the same as the number of symmetric Schröder paths of length n-1. For each k ≥ 3 we determine the generating function for the number of involutions avoiding the subsequences in A κ, according to length, first entry and number of fixed points.
Original language | English |
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State | Published - 2007 |
Event | 19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07 - Tianjin, China Duration: 2 Jul 2007 → 6 Jul 2007 |
Conference
Conference | 19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07 |
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Country/Territory | China |
City | Tianjin |
Period | 2/07/07 → 6/07/07 |
Keywords
- Forbidden subsequences
- Involutions
- Schröder paths
- Symmetric Schröder paths
ASJC Scopus subject areas
- Algebra and Number Theory