Sorting and preimages of pattern classes

Anders Claesson; Henning Úlfarsson

Sorting and preimages of pattern classes

Anders Claesson, Henning Úlfarsson

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

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.

Original language	English
Title of host publication	24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Place of Publication	Nancy, France
Pages	595-606
Number of pages	12
Publication status	Published - 2012

Keywords

sorting operations
stack-sort
bubble-sort
sorting algorithm
pattern classes

Cite this

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AB - 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.

KW - sorting operations

KW - stack-sort

KW - bubble-sort

KW - sorting algorithm

KW - pattern classes

UR - http://www.dmtcs.org/dmtcs-ojs/index.php/proceedings/article/view/dmAR0153

UR - http://www.dmtcs.org/dmtcs-ojs/index.php/proceedings/issue/view/126

M3 - Chapter

SP - 595

EP - 606

BT - 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)

CY - Nancy, France

ER -

Sorting and preimages of pattern classes

Abstract

Keywords

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