On the weighted enumeration of alternating sign matrices and descending plane partitions

Understand

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 nxn 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 (DPPs) for which each part is at most n and there are exactly k parts equal to n, m special parts and p nonspecial parts.