Geodesic
Three generalizations of Weyl's denominator formula
The electronic journal of combinatorics, Tome 3 (1996) no. 1

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Zbl EuDML
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.
DOI : 10.37236/1236
Classification : 05A19
Mots-clés : identities, Weyl's denominator, polynomials, digraphs, sum, product 
Todd Simpson. Three generalizations of Weyl's denominator formula. The electronic journal of combinatorics, Tome 3 (1996) no. 1. doi: 10.37236/1236
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     author = {Todd Simpson},
     title = {Three generalizations of {Weyl's} denominator formula},
     journal = {The electronic journal of combinatorics},
     year = {1996},
     volume = {3},
     number = {1},
     doi = {10.37236/1236},
     zbl = {0851.05009},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1236/}
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