The missing lemma for the modulo 23 Schröter–Russell–Ramanujan identity

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Let N0=3N_0=3, t=12t=12, C1=⋯=C12=46C_1=\dots=C_{12}=46, and m=3m=3. Set

(A1,…,A12)=(1,3,5,7,9,11,13,15,17,19,21,23),(A_1,\dots,A_{12})=(1,3,5,7,9,11,13,15,17,19,21,23), (B1,…,B12)=(0,2,4,6,8,10,12,14,16,18,20,22).(B_1,\dots,B_{12})=(0,2,4,6,8,10,12,14,16,18,20,22).

The missing lemma. Condition (i) of Theorem holds for these parameters.

A bijective proof would complete the unified combinatorial approach to the five Schröter, Russell and Ramanujan type identities by yielding a bijective proof of the identity modulo 23, which is otherwise proved analytically in the cited work.

References

Primary source

Colin Sandon and Fabrizio Zanello, “Warnaar's bijection and colored partition identities, I”, arXiv:1112.2637 (2012).

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