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Abstract for Todd Simpson, Three generalizations of Weyl's denominator formula

We give combinatorial proofs of three identities, each of which
generalizes Weyl's denominator formula for two of the three root
systems $B_n$, $C_n$, $D_n$. Two
of the three identities are due to S. Okada; the third appears in
the author's doctoral thesis, upon which this work is based.

Each of the identities we prove has a ``sum side'' and a
``product side''; both sides are polynomials in several commuting
indeterminates. We use weighted digraphs to represent the terms on
each side; the set of such digraphs that corresponds to the sum side
is a proper subset of the set corresponding to the product side.

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