7,756 research outputs found
New proofs of determinant evaluations related to plane partitions
We give a new proof of a determinant evaluation due to Andrews, which has
been used to enumerate cyclically symmetric and descending plane partitions. We
also prove some related results, including a q-analogue of Andrews's
determinant.Comment: 25 page
Elliptic pfaffians and solvable lattice models
We introduce and study twelve multivariable theta functions defined by
pfaffians with elliptic function entries. We show that, when the crossing
parameter is a cubic root of unity, the domain wall partition function for the
eight-vertex-solid-on-solid model can be written as a sum of two of these
pfaffians. As a limit case, we express the domain wall partition function for
the three-colour model as a sum of two Hankel determinants. We also show that
certain solutions of the TQ-equation for the supersymmetric eight-vertex model
can be expressed in terms of elliptic pfaffians.Comment: 34 page
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