##
Mihai Ciucu
and Christian Krattenthaler

# A factorization theorem for lozenge tilings of a hexagon with triangular holes

### (20 pages)

**Abstract.**
In this paper we present a combinatorial generalization of the fact
that the number of plane partitions that fit in a
2*a* x *b* x *b*
box is equal to the number of such plane partitions that are
symmetric, times the number of such plane partitions for which the
transpose is the same as the complement. We use the equivalent
phrasing of this identity in terms of symmetry classes of lozenge
tilings of a hexagon on the triangular lattice. Our generalization
consists of allowing the hexagon have certain symmetrically placed
holes along its horizontal symmetry axis. The special case when there
are no holes can be viewed as a new, simpler proof of the enumeration
of symmetric plane partitions.

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