Bijections, generalizations, and other properties of sequentially congruent partitions. (English) Zbl 07811999
This article offers a fresh perspective on partition theory by focusing on a newly defined class of partitions called sequentially congruent partitions, introduced by M. Schneider and R. Schneider [Ann. Comb. 23, No. 3–4, 1027–1037 (2019; Zbl 1437.11147)]. In sequentially congruent partitions, each part is congruent to the next part modulo its index. The paper extends the foundational work of Schneider and Schneider [loc. cit.] by providing new notations, generalizations, and bijections, as well as reinterpreting these partitions within the framework of Young diagram transformations. Additionally, the authors investigate how these partitions fit within theory of partition ideals of G. E. Andrews [in: Groupe d’Etude d’Algebre, 1re Annee 1975/76, Exp. 6, 8 p. (1978; Zbl 0383.10008)], yielding insights into the structure and properties of these partitions.
Reviewer: Mircea Merca (București)
MSC:
| 11P83 | Partitions; congruences and congruential restrictions |
| 05A17 | Combinatorial aspects of partitions of integers |
| 11P84 | Partition identities; identities of Rogers-Ramanujan type |
References:
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