论文信息 - Sorting and preimages of pattern classes

Sorting and preimages of pattern classes

We introduce an algorithm to determine when a sorting operation, such as stack-sort or bubble-sort, outputs a given pattern. The algorithm provides a new proof of the description of West-2-stack-sortable permutations, that is permutations that are completely sorted when passed twice through a stack, in terms of patterns. We also solve the long-standing problem of describing West-3-stack-sortable permutations. This requires a new type of generalized permutation pattern we call a decorated pattern.

Anders Claesson | Henning Úlfarsson | Henning Úlfarsson | Anders Claesson

[1] M. Albert,et al. On the inverse image of pattern classes under bubble sort , 2010, 1008.5299.

[2] Anders Claesson,et al. Mesh Patterns and the Expansion of Permutation Statistics as Sums of Permutation Patterns , 2011, Electron. J. Comb..

[3] Julian West,et al. Permutations with forbidden subsequences, and, stack-sortable permutations , 1990 .

[4] Henning Úlfarsson,et al. A unification of permutation patterns related to Schubert varieties , 2010, 1002.4361.

[5] Miklós Bóna,et al. A Survey of Stack-Sorting Disciplines , 2003, Electron. J. Comb..

[6] Serge Dulucq,et al. Permutations with forbidden subsequences and nonseparable planar maps , 1996, Discret. Math..

[7] Donald Ervin Knuth,et al. The Art of Computer Programming , 1968 .

[8] Henning Ulfarsson. Describing West-3-stack-sortable permutations with permutation patterns , 2011 .

[9] M. Bouvel,et al. Enumeration of permutations sorted with two passes through a stack and D_8 symmetries , 2012 .

[10] Doron Zeilberger,et al. A proof of Julian West's conjecture that the number of two-stacksortable permutations of length n is 2(3n)!/((n + 1)!(2n + 1)!) , 1992, Discret. Math..