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 $a_r,\dots,a_1,b_1,\dots,b_{n-r}$ such that $r\ge a_r\ge \cdots \ge a_1\ge 0 \ge b_1\ge \cdots \ge b_{n-r}\ge -(n-r)$, where $n\ge r\ge 0$, and when $X$ is the sub-lattice $P(n,d,r)$ of all the signed integer partitions of $P(n,r)$ having exactly $d$ non-zero parts.
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 $a_r,\dots,a_1,b_1,\dots,b_{n-r}$ such that $r\ge a_r\ge \cdots \ge a_1\ge 0 \ge b_1\ge \cdots \ge b_{n-r}\ge -(n-r)$, where $n\ge r\ge 0$, and when $X$ is the sub-lattice $P(n,d,r)$ of all the signed integer partitions of $P(n,r)$ having exactly $d$ non-zero parts.
Parallel Rank of Two Sandpile Models of Signed Integer Partitions
CHIASELOTTI, Giampiero;MARINO, Giuseppe;OLIVERIO, Paolo Antonio
2013-01-01
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 $a_r,\dots,a_1,b_1,\dots,b_{n-r}$ such that $r\ge a_r\ge \cdots \ge a_1\ge 0 \ge b_1\ge \cdots \ge b_{n-r}\ge -(n-r)$, where $n\ge r\ge 0$, and when $X$ is the sub-lattice $P(n,d,r)$ of all the signed integer partitions of $P(n,r)$ having exactly $d$ non-zero parts.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.