New combinatorial interpretations of some Rogers-Ramanujan type identities
Keywords:$(n t)$-color partitions, lattice paths, associated lattice paths, Bender-Knuth matrices, combinatorial identities
AbstractIn present paper, three Rogers-Ramanujan type identities are interpreted combinatorially in terms of certain associated lattice path functions. Out of these three identities, two are further explored using the Bender-Knuth matrices. These results give new combinatorial interpretations of these basic series identities. Using a bijection between the associated lattice path functions and the ($n+t$)-color partitions and that of between the associated lattice path functions and the weighted lattice path functions, we extend the recent work of Sareen and Rana to three new 5-way combinatorial identities. By using the bijection between Bender-Knuth matrices and the $n$-color partitions, we further extend their work to two new 6-way combinatorial identities.
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