Sandpiles and order structure of integer partitions

Eric Goles; Michel Morvan; Ha Duong Phan

doi:10.1016/S0166-218X(01)00178-0

Sandpiles and order structure of integer partitions

Eric Goles, Michel Morvan, Ha Duong Phan

Research output: Contribution to journal › Article › peer-review

35 Scopus citations

Abstract

In this paper, we study the orders obtained by the generalized dynamics of the sand piles model (SPM). We show that these orders are suborders of L _B, lattice of integer partitions introduced in Brylawski (Discrete Math. 6 (1973) 201), and we deduce from that a characterization of their fixed point. We prove that these orders form an increasing sequence of lattices from SPM to L _B. We then characterize longest paths in these lattices and give a formula describing their length.

Original language	English
Pages (from-to)	51-64
Number of pages	14
Journal	Discrete Applied Mathematics
Volume	117
Issue number	1-3
DOIs	https://doi.org/10.1016/S0166-218X(01)00178-0
State	Published - 15 Mar 2002
Externally published	Yes

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title = "Sandpiles and order structure of integer partitions",

abstract = "In this paper, we study the orders obtained by the generalized dynamics of the sand piles model (SPM). We show that these orders are suborders of L B, lattice of integer partitions introduced in Brylawski (Discrete Math. 6 (1973) 201), and we deduce from that a characterization of their fixed point. We prove that these orders form an increasing sequence of lattices from SPM to L B. We then characterize longest paths in these lattices and give a formula describing their length.",

author = "Eric Goles and Michel Morvan and Phan, {Ha Duong}",

note = "Funding Information: This work was done during M.M and H.D.P's visit at Departamento de Ingenier{\'ı}a Matem{\'a}tica, Universidad de Chile and was supported by Project ECOS-C96E02 and Chilean program FONDAP in Applied Mathematics (E.G., M.M., H.D.P.) ",

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AU - Goles, Eric

AU - Morvan, Michel

AU - Phan, Ha Duong

N1 - Funding Information: This work was done during M.M and H.D.P's visit at Departamento de Ingenierı́a Matemática, Universidad de Chile and was supported by Project ECOS-C96E02 and Chilean program FONDAP in Applied Mathematics (E.G., M.M., H.D.P.)

PY - 2002/3/15

Y1 - 2002/3/15

N2 - In this paper, we study the orders obtained by the generalized dynamics of the sand piles model (SPM). We show that these orders are suborders of L B, lattice of integer partitions introduced in Brylawski (Discrete Math. 6 (1973) 201), and we deduce from that a characterization of their fixed point. We prove that these orders form an increasing sequence of lattices from SPM to L B. We then characterize longest paths in these lattices and give a formula describing their length.

AB - In this paper, we study the orders obtained by the generalized dynamics of the sand piles model (SPM). We show that these orders are suborders of L B, lattice of integer partitions introduced in Brylawski (Discrete Math. 6 (1973) 201), and we deduce from that a characterization of their fixed point. We prove that these orders form an increasing sequence of lattices from SPM to L B. We then characterize longest paths in these lattices and give a formula describing their length.

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VL - 117

SP - 51

EP - 64

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

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ER -

Sandpiles and order structure of integer partitions

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