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A natural extension of the Young partition lattice. (English) Zbl 1317.05018

Summary: Recently G. E. Andrews [Bull. Am. Math. Soc., New Ser. 44, No. 4, 561–573 (2007; Zbl 1172.11031)] introduced the concept of signed partition: a signed partition is a finite sequence of integers \(a_{k}, \ldots, a_{1}, a_{-1}, \ldots, a_{-l}\) such that \(a_{k} \geq \ldots \geq a_{1} > 0 > a_{-1} \geq \ldots \geq a_{-l}\). So far the signed partitions have been studied from an arithmetical point of view. In this paper we first generalize the concept of signed partition and we next use such a generalization to introduce a partial order on the set of all the signed partitions. Furthermore, we show that this order has many remarkable properties and that it generalizes the classical order on the Young lattice.

MSC:

05A17 Combinatorial aspects of partitions of integers
11P81 Elementary theory of partitions

Citations:

Zbl 1172.11031
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