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

O. Foda·S. O. Warnaar
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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 $χ_{1,1}^{(p,p+1)}(q)$ Virasoro characters, conjectured by the Stony Brook group.

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O. Foda, S. O. Warnaar. 1995-01-20. A bijection which implies Melzer's polynomial identities: the $χ_{1,1}^{(p,p+1)}$ case. https://doi.org/10.1007/bf00714377

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