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

preprint1995arXivOpen access

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

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A bijection which implies Melzer's polynomial identities: the χ1,1(p,p+1)χ_{1,1}^{(p,p+1)}χ1,1(p,p+1)​ case

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