Mihai Ciucu and Christian Krattenthaler

Plane partitions II: 5 1/2 symmetry classes

(18 pages)

Abstract. We present new, simple proofs for the enumeration of five of the ten symmetry classes of plane partitions contained in a given box. Four of them are derived from a simple determinant evaluation, using combinatorial arguments. The previous proofs of these four cases were quite complicated. For one more symmetry class we give an elementary proof in the case when two of the sides of the box are equal. Our results include simple evaluations of the determinants det ( \deltaij + \binom {x+i+j} {i} ) 0<=i,j<=n-1 and det ( \binom {x+i+j} {2j-i} ) 0<=i,j<=n-1, notorious in plane partitions enumeration, whose previous evaluations were quite intricate.

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