Posets of matrices, and permutations with forbidden subsequences

Ray, Nigel and West, Julian (2003) Posets of matrices, and permutations with forbidden subsequences. Annals of Combinatorics, 7 (1). pp. 55-88. ISSN 0219-3094

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Abstract

Abstract. The enumeration of permutations with specific forbidden subsequences has applications in areas ranging from algebraic geometry to the study of sorting algorithms. We consider a ranked poset of permutation matrices whose global structure incorporates the solution to the equivalent problem of enumerating permutations which contain a required subsequence. We describe this structure completely for saturated chains of lengths one and two, so settling several new and general instances of the original problem, and conclude with a superficial asymptotic investigation of arbitrary chains whose length is small by comparison with the rank of its constituent permutations. The value of this approach is reflected in the appearance of closed polynomial formulae (related to the Robinson-Schensted correspondence) and of a framework for the systematic analysis of associated combinatorial questions; indeed, we begin by studying a simpler poset of 0-1 sequences as the natural environment in which to introduce our insertion and deletion operators.

Item Type:	Article
Uncontrolled Keywords:	permutations, forbidden subsequences, permutation matrices, posets, enumeration
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 05 Combinatorics
Depositing User:	Ms Lucy van Russelt
Date Deposited:	21 Sep 2006
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/609

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