Proof of George Andrews’s and David Robbins’s q-TSPP conjecture

The conjecture that the orbit-counting generating function for totally symmetric plane partitions can be written as an explicit product formula has been stated independently by George Andrews and David Robbins around 1983. We present a proof of this long-standing conjecture.

[1]  Souichi Okada,et al.  On the generating functions for certain classes of plane partitions , 1989, J. Comb. Theory, Ser. A.

[2]  Richard P. Stanley,et al.  Symmetries of plane partitions , 1986, J. Comb. Theory A.

[3]  Frédéric Chyzak,et al.  An extension of Zeilberger's fast algorithm to general holonomic functions , 2000, Discret. Math..

[4]  Guo-Niu Han,et al.  The Andrews Festschrift , 2001 .

[5]  Nobuki Takayama,et al.  Gröbner basis, integration and transcendental functions , 1990, ISSAC '90.

[6]  D. Zeilberger,et al.  A Proof of George Andrews' and Dave Robbins' q-TSPP Conjecture (modulo a finite amount of routine calculations) , 2008, 0808.0571.

[7]  C. Krattenthaler.  ADVANCED DETERMINANT CALCULUS , 1999, math/9902004.

[8]  D. Zeilberger.  A holonomic systems approach to special functions identities , 1990 .

[9]  Peter McMullen,et al.  Constructions for regular polytopes , 1990, J. Comb. Theory, Ser. A.

[10]  Bruno Salvy,et al.  Non-Commutative Elimination in Ore Algebras Proves Multivariate Identities , 1998, J. Symb. Comput..

[11]  Doron Zeilberger.  The Holonomic Ansatz II. Automatic Discovery(!) And Proof(!!) of Holonomic Determinant Evaluations , 2007 .

[12]  George E. Andrews,et al.  Plane partitions VI: Stembridge's TSPP theorem , 2005, Adv. Appl. Math..

[13]  Christoph Koutschan,et al.  Advanced applications of the holonomic systems approach , 2010, ACCA.

[14]  John R. Stembridge.  The Enumeration of Totally Symmetric Plane Partitions , 1995 .

[15]  Richard P. Stanley,et al.  A Baker's dozen of conjectures concerning plane partitions , 1986 .

[16]  Christoph Koutschan,et al.  Eliminating Human Insight: An Algorithmic Proof of Stembridge's TSPP Theorem , 2009, ArXiv.