Parallel Rank of Two Sandpile Models of Signed Integer Partitions

G. Chiaselotti, T. Gentile, G. Marino and P. A. Oliverio

Journal of Applied Mathematics, 2013, vol. 2013, issue 1

Abstract: We introduce the concept of fundamental sequence for a finite graded poset X which is also a discrete dynamical model. The concept of fundamental sequence is a refinement of the concept of parallel convergence time for these models. We compute the parallel convergence time and the fundamental sequence when X is the finite lattice P(n, r) of all the signed integer partitions ar, …, a1, b1, …, bn−r such that r ≥ ar ≥ ⋯≥a1 ≥ 0 ≥ b1 ≥ ⋯≥bn−r ≥ −(n − r), where n ≥ r ≥ 0, and when X is the sublattice P(n, d, r) of all the signed integer partitions of P(n, r) having exactly d nonzero parts.

Date: 2013
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https://doi.org/10.1155/2013/292143

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2013:y:2013:i:1:n:292143

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