Plane partitions VI: Stembridge's TSPP theorem

George E. Andrews; Peter Paule; Carsten Schneider

doi:10.1016/j.aam.2004.07.008

Plane partitions VI: Stembridge's TSPP theorem

George E. Andrews, Peter Paule, Carsten Schneider

Mathematics

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

We provide a new proof of Stembridge's theorem which validated the Totally Symmetric Plane Partitions (TSPP) Conjecture. The overall strategy of our proof follows the same general pattern of determinant evaluation as discussed by the first named author in a series of papers. The resulting hypergeometric multiple sum identities turn out to be quite complicated. Their correctness is proved by applying new algorithmic methods from symbolic summation.

Original language	English (US)
Pages (from-to)	709-739
Number of pages	31
Journal	Advances in Applied Mathematics
Volume	34
Issue number	4 SPEC. ISS.
DOIs	https://doi.org/10.1016/j.aam.2004.07.008
State	Published - May 2005

All Science Journal Classification (ASJC) codes

Applied Mathematics

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10.1016/j.aam.2004.07.008

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title = "Plane partitions VI: Stembridge's TSPP theorem",

abstract = "We provide a new proof of Stembridge's theorem which validated the Totally Symmetric Plane Partitions (TSPP) Conjecture. The overall strategy of our proof follows the same general pattern of determinant evaluation as discussed by the first named author in a series of papers. The resulting hypergeometric multiple sum identities turn out to be quite complicated. Their correctness is proved by applying new algorithmic methods from symbolic summation.",

author = "Andrews, {George E.} and Peter Paule and Carsten Schneider",

note = "Funding Information: * Corresponding author. E-mail addresses: [email protected] (G.E. Andrews), [email protected] (P. Paule), [email protected] (C. Schneider). 1 The author was partially supported by National Science Foundation Grant DMS. 2 The author was partially supported by the SFB-grant F1305 of the Austrian FWF. 3 The author was supported by the Austrian Academy of Sciences and by grant P16613-N12 of the Austrian FWF.",

year = "2005",

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TY - JOUR

T1 - Plane partitions VI

T2 - Stembridge's TSPP theorem

AU - Andrews, George E.

AU - Paule, Peter

AU - Schneider, Carsten

N1 - Funding Information: * Corresponding author. E-mail addresses: [email protected] (G.E. Andrews), [email protected] (P. Paule), [email protected] (C. Schneider). 1 The author was partially supported by National Science Foundation Grant DMS. 2 The author was partially supported by the SFB-grant F1305 of the Austrian FWF. 3 The author was supported by the Austrian Academy of Sciences and by grant P16613-N12 of the Austrian FWF.

PY - 2005/5

Y1 - 2005/5

N2 - We provide a new proof of Stembridge's theorem which validated the Totally Symmetric Plane Partitions (TSPP) Conjecture. The overall strategy of our proof follows the same general pattern of determinant evaluation as discussed by the first named author in a series of papers. The resulting hypergeometric multiple sum identities turn out to be quite complicated. Their correctness is proved by applying new algorithmic methods from symbolic summation.

AB - We provide a new proof of Stembridge's theorem which validated the Totally Symmetric Plane Partitions (TSPP) Conjecture. The overall strategy of our proof follows the same general pattern of determinant evaluation as discussed by the first named author in a series of papers. The resulting hypergeometric multiple sum identities turn out to be quite complicated. Their correctness is proved by applying new algorithmic methods from symbolic summation.

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JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

IS - 4 SPEC. ISS.

ER -

Plane partitions VI: Stembridge's TSPP theorem

Abstract

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