A unification of permutation patterns related to Schubert varieties

Henning A. Úlfarsson

A unification of permutation patterns related to Schubert varieties

Henning A. Úlfarsson^*

^*Corresponding author for this work

Department of Computer Science

Research output: Contribution to conference › Paper › peer-review

Abstract

We prove new connections between permutation patterns and singularities of Schubert varieties, by giving a new characterization of factorial and Gorenstein varieties in terms of so called bivincular patterns. These are generalizations of classical patterns where conditions are placed on the location of an occurrence in a permutation, as well as on the values in the occurrence. This clarifies what happens when the requirement of smoothness is weakened to factoriality and further to Gorensteinness, extending work of Bousquet-Mélou and Butler (2007), and Woo and Yong (2006). We also prove results that translate some known patterns in the literature into bivincular patterns.

Original language	English
Pages	1057-1068
Number of pages	12
Publication status	Published - 2010
Event	22nd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'10 - San Francisco, CA, United States Duration: 2 Aug 2010 → 6 Aug 2010

Conference

Conference	22nd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'10
Country/Territory	United States
City	San Francisco, CA
Period	2/08/10 → 6/08/10

Other keywords

Patterns
Permutations
Schubert varieties
Singularities

Cite this

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title = "A unification of permutation patterns related to Schubert varieties",

abstract = "We prove new connections between permutation patterns and singularities of Schubert varieties, by giving a new characterization of factorial and Gorenstein varieties in terms of so called bivincular patterns. These are generalizations of classical patterns where conditions are placed on the location of an occurrence in a permutation, as well as on the values in the occurrence. This clarifies what happens when the requirement of smoothness is weakened to factoriality and further to Gorensteinness, extending work of Bousquet-M{\'e}lou and Butler (2007), and Woo and Yong (2006). We also prove results that translate some known patterns in the literature into bivincular patterns.",

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AU - Úlfarsson, Henning A.

PY - 2010

Y1 - 2010

N2 - We prove new connections between permutation patterns and singularities of Schubert varieties, by giving a new characterization of factorial and Gorenstein varieties in terms of so called bivincular patterns. These are generalizations of classical patterns where conditions are placed on the location of an occurrence in a permutation, as well as on the values in the occurrence. This clarifies what happens when the requirement of smoothness is weakened to factoriality and further to Gorensteinness, extending work of Bousquet-Mélou and Butler (2007), and Woo and Yong (2006). We also prove results that translate some known patterns in the literature into bivincular patterns.

AB - We prove new connections between permutation patterns and singularities of Schubert varieties, by giving a new characterization of factorial and Gorenstein varieties in terms of so called bivincular patterns. These are generalizations of classical patterns where conditions are placed on the location of an occurrence in a permutation, as well as on the values in the occurrence. This clarifies what happens when the requirement of smoothness is weakened to factoriality and further to Gorensteinness, extending work of Bousquet-Mélou and Butler (2007), and Woo and Yong (2006). We also prove results that translate some known patterns in the literature into bivincular patterns.

KW - Patterns

KW - Permutations

KW - Schubert varieties

KW - Singularities

UR - http://www.scopus.com/inward/record.url?scp=84860515202&partnerID=8YFLogxK

M3 - Paper

AN - SCOPUS:84860515202

SP - 1057

EP - 1068

T2 - 22nd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'10

Y2 - 2 August 2010 through 6 August 2010

ER -

A unification of permutation patterns related to Schubert varieties

Abstract

Conference

Other keywords

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