A bijection which implies Melzer's polynomial identities: the ${\chi }_{1,1}^{(p,p+1)}$ case

Abstract

We obtain a bijection between certain lattice paths and partitions. This implies a proof of polynomial identities conjectured by Melzer. In a limit, these identities reduce to Rogers--Ramanujan-type identities for the ${\chi }_{1,1}^{(p,p+1)}(q)$ Virasoro characters, conjectured by the Stony Brook group.

10 pages, latex, 3 figures

References in corpus (4)

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• Fermionic counting of RSOS-states and Virasoro character formulas for the unitary minimal series M(ν,ν+1). Exact results
• Fermionic Character Sums and the Corner Transfer Matrix
• Quasi-Particles, Conformal Field Theory, and $q$-Series

Cited by in corpus (8)

• Fermionic solution of the Andrews-Baxter-Forrester model II: proof of Melzer's polynomial identities
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• Multinomials and Polynomial Bosonic Forms for the Branching Functions of the $\widehat{su}(2{)}_M\times \widehat{su}(2{)}_N/\widehat{su}(2{)}_{M+N}$ Conformal Coset Models
• Bailey flows and Bose-Fermi identities for the conformal coset models $(A_1^{(1)}{)}_N\times (A_1^{(1)}{)}_{N^{\prime }}/(A_1^{(1)}{)}_{N+N^{\prime }}$
• Non-abelian Exclusion Statistics
• Strings, paths, and standard tableaux
• Closed form fermionic expressions for the Macdonald index