A natural extension of the Young partition lattice

Author:

Bisi Cinzia1,Chiaselotti Giampiero2,Marino Giuseppe2,Oliverio Paolo Antonio2

Affiliation:

1. Dipartimento di Matematica ed Informatica, Universitá di Ferrara, Via Machiavelli 35, 44121 Ferrara, Italy

2. Dipartimento di Matematica, Universitá della Calabria, Via Pietro Bucci, Cubo 30B, 87036 Arcavacata di Rende (CS), Italy

Abstract

Abstract Recently Andrews introduced the concept of signed partition: a signed partition is a finite sequence of integers ak, . . . , a1, a−1, . . . , a−l such that ak ≥ ... ≥ a1 > 0 > a−1 ≥ ... ≥ 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.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

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