Plane partitions. VI: Stembridge's TSPP theorem

DOI10.1016/j.aam.2004.07.008zbMath1066.05019OpenAlexW2075531801MaRDI QIDQ2483909

Carsten Schneider, George E. Andrews, Paule, Peter

Publication date: 1 August 2005

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aam.2004.07.008

zbMATH Keywords

hypergeometric multiple sum identities

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17)

Related Items (19)

Hypergeometric summation algorithms for high-order finite elements ⋮ Some useful theorems for asymptotic formulas and their applications to skew plane partitions and cylindric partitions ⋮ Interview with Peter Paule ⋮ Proof of George Andrews’s and David Robbins’s q -TSPP conjecture ⋮ ARITHMETIC PROPERTIES OF 1-SHELL TOTALLY SYMMETRIC PLANE PARTITIONS ⋮ Plane partitions. VI: Stembridge's TSPP theorem ⋮ A new Sigma approach to multi-summation ⋮ A NEW CONGRUENCE MODULO 25 FOR 1-SHELL TOTALLY SYMMETRIC PLANE PARTITIONS ⋮ Gaussian Hypergeometric series and supercongruences ⋮ Congruences for 1-shell totally symmetric plane partitions ⋮ Creative telescoping on multiple sums ⋮ Extended Zeilberger's algorithm for identities on Bernoulli and Euler polynomials ⋮ NEW INFINITE FAMILIES OF CONGRUENCES MODULO 4 AND 8 FOR 1-SHELL TOTALLY SYMMETRIC PLANE PARTITIONS ⋮ Computer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order ⋮ Creative Telescoping for Holonomic Functions ⋮ A case study for \(\zeta (4)\) ⋮ Term Algebras, Canonical Representations and Difference Ring Theory for Symbolic Summation ⋮ Degree bounds to find polynomial solutions of parameterized linear difference equations in \(\Pi\Sigma\)-fields ⋮ The SAGEX review on scattering amplitudes Chapter 4: Multi-loop Feynman integrals

Uses Software

• gfun
• QEPCAD
• SIGMA
• GeneratingFunctions

Cites Work

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• Symmetries of plane partitions
• Plane partitions. IV: A conjecture of Mills-Robbins-Rumsey
• On the generating functions for certain classes of plane partitions
• Plane partitions. III: The weak Macdonald conjecture
• Differentiably finite power series
• Partial cylindrical algebraic decomposition for quantifier elimination
• Plane partitions. II: The equivalence of the Bender-Knuth and MacMahon conjectures
• Plane partitions. V: The TSSCPP conjecture
• Computer proofs of a new family of harmonic number identities.
• The enumeration of totally symmetric plane partitions
• An extension of Zeilberger's fast algorithm to general holonomic functions
• Plane partitions. VI: Stembridge's TSPP theorem
• A new Sigma approach to multi-summation
• GFUN
• Rational solutions of linear differential and difference equations with polynomial coefficients

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