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A natural extension of the Young partition lattice
-
Cinzia Bisi
,
Giampiero Chiaselotti
Published/Copyright:
July 3, 2015
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.
Keywords
Graded lattices, integer partitions, Young diagrams, sand piles models
Received: 2013-4-30
Published Online: 2015-7-3
Published in Print: 2015-7-1
© 2015 by Walter de Gruyter Berlin/Boston
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- A natural extension of the Young partition lattice
- Pencils of small degree on curves on unnodal Enriques surfaces
- Michael’s Selection Theorem in a semilinear context
- Quasi-simple Lie groups as multiplication groups of topological loops
- Some spectral results on Kakeya sets
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Articles in the same Issue
- Frontmatter
- A natural extension of the Young partition lattice
- Pencils of small degree on curves on unnodal Enriques surfaces
- Michael’s Selection Theorem in a semilinear context
- Quasi-simple Lie groups as multiplication groups of topological loops
- Some spectral results on Kakeya sets
- Projective normality and the generation of the ideal of an Enriques surface
- Topological contact dynamics I: symplectization and applications of the energy-capacity inequality
- Torsion-free G*2(2)-structures with full holonomy on nilmanifolds
