作品的场地周界

IF 0.3 Q4 MATHEMATICS, APPLIED

Discrete Mathematics and Applications Pub Date : 2022-04-01 DOI:10.1515/dma-2022-0007

A. Blecher, C. Brennan, A. Knopfmacher

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引用次数: 0

摘要

n的组合是正整数(σi)i=1k $\begin{array}{} (\sigma_i)_{i = 1}^k \end{array} $的有限序列，使得σ1+σ2+⋯+σk=n。$$\begin{array}{} \sigma_1+\sigma_2+\cdots +\sigma_k = n. \end{array} $$我们将n的组合表示为面积为n的柱状图，使得柱状图的第i列的高度等于组合的第i部分的大小。我们考虑场地周长，即多聚体边界外最近邻细胞的数量。得到了计算组合物总场地周长的生成函数。此外，我们通过直接计数重新推导出一个组合的平均场地周长。最后，我们确定了具有给定半周长的柱状图的平均点周长。

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The site-perimeter of compositions

Abstract Compositions of n are finite sequences of positive integers (σi)i=1k $\begin{array}{} (\sigma_i)_{i = 1}^k \end{array} $ such that σ1+σ2+⋯+σk=n. $$\begin{array}{} \sigma_1+\sigma_2+\cdots +\sigma_k = n. \end{array} $$ We represent a composition of n as a bargraph with area n such that the height of the i-th column of the bargraph equals the size of the i-th part of the composition. We consider the site-perimeter which is the number of nearest-neighbour cells outside the boundary of the polyomino. The generating function that counts the total site-perimeter of compositions is obtained. In addition, we rederive the average site-perimeter of a composition by direct counting. Finally we determine the average site-perimeter of a bargraph with a given semi-perimeter.

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来源期刊

Discrete Mathematics and Applications MATHEMATICS, APPLIED-

CiteScore

0.60

自引率

20.00%

发文量

期刊介绍： The aim of this journal is to provide the latest information on the development of discrete mathematics in the former USSR to a world-wide readership. The journal will contain papers from the Russian-language journal Diskretnaya Matematika, the only journal of the Russian Academy of Sciences devoted to this field of mathematics. Discrete Mathematics and Applications will cover various subjects in the fields such as combinatorial analysis, graph theory, functional systems theory, cryptology, coding, probabilistic problems of discrete mathematics, algorithms and their complexity, combinatorial and computational problems of number theory and of algebra.