Forbidden Configurations in Discrete Geometry

David Eppstein

  • 出版商: Cambridge
  • 出版日期: 2018-05-17
  • 售價: $1,940
  • 貴賓價: 9.5$1,843
  • 語言: 英文
  • 頁數: 238
  • 裝訂: Paperback
  • ISBN: 1108439136
  • ISBN-13: 9781108439138
  • 相關分類: 離散數學 Discrete-mathematics
  • 立即出貨 (庫存=1)

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商品描述

This book surveys the mathematical and computational properties of finite sets of points in the plane, covering recent breakthroughs on important problems in discrete geometry, and listing many open problems. It unifies these mathematical and computational views using forbidden configurations, which are patterns that cannot appear in sets with a given property, and explores the implications of this unified view. Written with minimal prerequisites and featuring plenty of figures, this engaging book will be of interest to undergraduate students and researchers in mathematics and computer science. Most topics are introduced with a related puzzle or brain-teaser. The topics range from abstract issues of collinearity, convexity, and general position to more applied areas including robust statistical estimation and network visualization, with connections to related areas of mathematics including number theory, graph theory, and the theory of permutation patterns. Pseudocode is included for many algorithms that compute properties of point sets.

商品描述(中文翻譯)

本書概述了平面上有限點集的數學和計算特性,涵蓋了離散幾何學中重要問題的最新突破,並列出了許多未解決的問題。它使用禁止配置統一了這些數學和計算觀點,禁止配置是指在具有特定屬性的集合中無法出現的模式,並探討了這種統一觀點的影響。本書以最少的先備知識為基礎,並配有大量圖片,對本科生和數學和計算機科學研究人員具有吸引力。大多數主題都以相關的謎題或腦筋急轉彎引入。這些主題涵蓋了從共線性、凸性和一般位置的抽象問題到更應用的領域,包括強健統計估計和網絡可視化,並與數論、圖論和排列模式理論等數學相關領域有關。書中還包含了許多計算點集屬性的算法的偽代碼。