An Introduction To The Theory Of Numbers Fourth Edition
An Introduction To The Theory Of Numbers Fourth Edition
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数论导论第四版
DOI：
10.1007/978-3-319-66396-8
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发表时间：
1968
影响因子：
0.9
通讯作者：
G. Hardy
中科院分区：
文献类型：
--
作者：
G. Hardy
数字凸（DC）集在数字几何的框架中起着重要的作用，当我们处理多项式时，它为欧几里得凸性的概念提供了一个自然的推广，即，有限且连通的点集。Brlek、Lachaud、Provençal和Reutenauer关于该主题的结果（参见[4]）在数字凸性和词的组合数学之间架起了一座桥梁：DCpolyomino的边界字可以被划分为四条单调路径，本文的目的是提供边界词必须满足的一些局部性质，以便允许单个点修改，保持凸的polyomino。
Digital convex (DC) sets plays a prominent role in the framework of digital geometry providing a natural generalization to the concept of Euclidean convexity when we are dealing with polyominoes, i.e., finite and connected sets of points. A result by Brlek, Lachaud, Provençal and Reutenauer (see [4]) on this topic sets a bridge between digital convexity and combinatorics on words: the boundary word of aDCpolyomino can be divided in four monotone paths, each of them having a Lyndon factorization that contains only Christoffel words.The intent of this paper is to provide some local properties that a boundary words has to fulfill in order to allow a single point modifications that preserves the convexity of the polyomino.