Enumerative combinatorics
New symmetric plane partition identities from invariant theory work of De Concini and Procesi
European Journal of Combinatorics
Schützenberger's jeu de taquin and plane partitions
Journal of Combinatorial Theory Series A
Proofs and confirmations: the story of the alternating sign matrix conjecture
Proofs and confirmations: the story of the alternating sign matrix conjecture
Concrete Math
Another refinement of the Bender-Knuth (ex-)conjecture
European Journal of Combinatorics
The operator formula for monotone triangles - simplified proof and three generalizations
Journal of Combinatorial Theory Series A
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We present an elementary method for proving enumeration formulas which are polynomials in certain parameters if others are fixed and factorize into distinct linear factors over Z. Roughly speaking the idea is to prove such formulas by "explaining" their zeros using an appropriate combinatorial extension of the objects under consideration to negative integer parameters. We apply this method to prove a new refinement of the Bender-Knuth (ex-)Conjecture, which easily implies the Bender-Knuth (ex-)Conjecture itself. This is probably the most elementary way to prove this result currently known. Furthermore we adapt our method to q-polynomials, which allows us to derive generating function results as well. Finally we use this method to give another proof for the enumeration of semistandard tableaux of a fixed shape which differs from our proof of the Bender-Knuth (ex-)Conjecture in that it is a multivariate application of our method.