A polynomial method for the enumeration of plane partitions and alternating sign matrices
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منابع مشابه
Truncated determinants and the refined enumeration of Alternating Sign Matrices and Descending Plane Partitions
In these notes, we will be mainly focussing on the proof of the so-called ASM-DPP conjecture of Mills, Robbins and Rumsey [22] which relates refined enumerations of Alternating Sign Matrices (ASM) and Descending Plane Partitions (DPP). ASMs were introduced by Mills, Robbins and Rumsey [24] in their study of Dodgsons condensation algorithm for the evaluation of determinants. DPPs were introduced...
متن کاملAlternating Sign Matrices and Descending Plane Partitions
An alternating sign matrix is a square matrix such that (i) all entries are 1,-1, or 0, (ii) every row and column has sum 1, and (iii) in every row and column the nonzero entries alternate in sign. Striking numerical evidence of a connection between these matrices and the descending plane partitions introduced by Andrews (Invent. Math. 53 (1979), 193-225) have been discovered, but attempts to p...
متن کاملOn the weighted enumeration of alternating sign matrices and descending plane partitions
We prove a conjecture of Mills, Robbins and Rumsey [Alternating sign matrices and descending plane partitions, J. Combin. Theory Ser. A 34 (1983), 340–359] that, for any n, k, m and p, the number of n × n alternating sign matrices (ASMs) for which the 1 of the first row is in column k + 1 and there are exactly m −1’s and m+ p inversions is equal to the number of descending plane partitions (DPP...
متن کاملOn refined enumerations of totally symmetric self-complementary plane partitions II
In this paper we settle a weak version of a conjecture (i.e. Conjecture 6) by Mills, Robbins and Rumsey in the paper “Self-complementary totally symmetric plane partitions” J. Combin. Theory Ser. A 42, 277–292. In other words we show that the number of shifted plane partitions invariant under the involution γ is equal to the number of alternating sign matrices invariant under the vertical flip....
متن کاملArithmetic Properties of Plane Partitions
The 2-adic valuations of sequences counting the number of alternating sign matrices of size n and the number of totally symmetric plane partitions are shown to be related in a simple manner.
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تاریخ انتشار 2005