Towards a combinatorial classification of skew Schur functions

McNamara, Peter R. W.; Willigenburg, Stephanie van

doi:10.1090/s0002-9947-09-04683-2

Cited by 18 publications

(21 citation statements)

References 17 publications

(39 reference statements)

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“…The problem under which conditions two skew diagrams give rise to the same skew character has recently seen much work (see for example [3] or [4]). We can use the theorems and remarks in Section 4 to give us conditions for two skew diagrams A, B to represent the same skew characters.…”

Section: On the Equality Of Skew Charactersmentioning

confidence: 99%

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On Principal Hook Length Partitions and Durfee Sizes in Skew Characters

Gutschwager

2011

Ann. Comb.

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We construct for a given arbitrary skew diagram A all partitions ν with maximal principal hook lengths among all partitions with [ν] appearing in [A]. Furthermore, we show that these are also partitions with minimal Durfee size. We use this to give the maximal Durfee size for [ν] appearing in [A] for the cases when A decays into two partitions and for some special cases of A. We also deduce necessary conditions for two skew diagrams to represent the same skew character.

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Section: On the Equality Of Skew Charactersmentioning

confidence: 99%

“…There has recently been much interest in the question of determining necessary or [2], [3], [4]. In Section 6, we use the results from Section 4 to give necessary conditions for two skew diagrams A and B to represent the same skew character, i.e., [A] = [B].…”

Section: Introductionmentioning

confidence: 99%

On Principal Hook Length Partitions and Durfee Sizes in Skew Characters

Gutschwager

2011

Ann. Comb.

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“…The question of when two skew diagrams yield equal skew Schur functions has been studied in detail; for instance, see [1], [8], and [9]. However, the related question of when two skew diagrams have the same Schur support (see Definition 2.1) has received less attention, with the most substantial progress occurring in [6] (2007) and in [7] (2011).…”

Section: Introductionmentioning

confidence: 99%

Support Equalities Among Ribbon Schur Functions

Gaetz

Hardt

Sridhar

2019

Electron. J. Combin.

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In 2007, McNamara proved that two skew shapes can have the same Schur support only if they have the same number of k × rectangles as subdiagrams. This implies that two ribbons can have the same Schur support only if one is obtained by permuting row lengths of the other. We present substantial progress towards classifying when a permutation π ∈ S m of row lengths of a ribbon α produces a ribbon α π with the same Schur support as α; when this occurs for all π ∈ S m , we say that α has full equivalence class. Our main results include a sufficient condition for a ribbon α to have full equivalence class. Additionally, we prove a separate necessary condition, which we conjecture to be sufficient.

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“…In this setting, equality among skew Schur functions corresponds to equivalence of certain GL N (C) modules [RSvW07]. Coincidences among skew Schur functions have been studied by Billera-Thomas-van Willigenburg [BTvW06], Reiner-Shaw-van Willigenburg [RSvW07], and McNamara-van Willigenburg [MVW09], among others.…”

Section: Introductionmentioning

confidence: 99%

Coincidences among skew stable and dual stable Grothendieck polynomials

Alwaise

Chen

Patrias

et al. 2018

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The question of when two skew Young diagrams produce the same skew Schur function has been well-studied. We investigate the same question in the case of stable Grothendieck polynomials, which are the K-theoretic analogues of the Schur functions. We prove a necessary condition for two skew shapes to give rise to the same dual stable Grothendieck polynomial. We also provide a necessary and sufficient condition in the case where the two skew shapes are ribbons.

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Towards a combinatorial classification of skew Schur functions

Cited by 18 publications

References 17 publications

On Principal Hook Length Partitions and Durfee Sizes in Skew Characters

On Principal Hook Length Partitions and Durfee Sizes in Skew Characters

Support Equalities Among Ribbon Schur Functions

Coincidences among skew stable and dual stable Grothendieck polynomials

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