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Laboratoire d'informatique fondamentale de Marseille UMR 6166 - CNRS, Université de la Méditerranée, Université de Provence |
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Laboratoire d'informatique fondamentale de Marseille UMR 6166 - CNRS, Université de la Méditerranée, Université de Provence |
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| HAL: hal-00142355, version 1 |
| arXiv: math.CO/0510098 |
| Detailed view |  Export this paper |
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| Order 24, 3 (2007) 155--179 |
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| Congruences of Multinomial Lattices |
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| Luigi Santocanale 1 |
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| (2007-11-15) |
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| We study the congruence lattices of the multinomial lattices L(v) introduced by Bennett and Birkhoff. Our main motivation is to investigate Parikh equivalence relations that model concurrent computation. We accomplish this goal by providing an explicit description of the join dependency relation between two join irreducible elements and of its reflexive transitive closure. The explicit description emphasizes several properties and makes it possible to separate the equational theories of multinomial lattices by their dimensions. In their covering of non modular varieties Jipsen and Rose define a sequence of equations SD_{n}(\land), for n \geq 0. Our main result sounds as follows: if v = (v_{1},...,v_{n}) \in N^{n} and v_{i} > 0 for i = 1,..., n, then the multinomial lattice L(v) satisfies SD_{n-1}(\land) and fails SD_{n-2}(\land). |
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| 1: | Laboratoire d'informatique Fondamentale de Marseille (LIF) |
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CNRS : UMR6166 – Université de la Méditerranée - Aix-Marseille II – Université de Provence - Aix-Marseille I |
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| Subject | : | Mathematics/Combinatorics Mathematics/Rings and Algebras |
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| lattices |
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| Fulltext link: |
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| http://fr.arXiv.org/abs/math.CO/0510098 |
| hal-00142355, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00142355 | |
| oai:hal.archives-ouvertes.fr:hal-00142355 | |
| From: Luigi Santocanale | |
| Submitted on: Wednesday, 18 April 2007 14:20:22 | |
| Updated on: Wednesday, 4 March 2009 18:04:31 | |
