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

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.

Sources & referencesView supporting material

Primary source

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

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