更恶毒的市长

IF 0.4 4区数学 Q4 MATHEMATICS

American Mathematical Monthly Pub Date : 2023-07-27 DOI:10.1080/00029890.2023.2231816

Reed Acton, T. K. Petersen, Blake Shirman, Daniel Toal, Francesco Laudano

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引用次数: 0

摘要

摘要在本文中，我们研究了彼得·温克勒的《数学谜题：鉴赏家的收藏》一书中所描述的恶意Maitre d’问题。这个问题是由计算机科学家Rob Pike引起的，涉及到让用餐者坐在一张圆桌周围，在每对相邻的桌子之间放置餐巾纸。领班的目标是让用餐者就座，以最大限度地增加到达餐桌的用餐者数量，他们发现餐巾放在自己位置的左右两侧，已经被邻居拿走了。温克勒为这个问题提出了一个他认为是最优的解决方案。我们使用枚举组合数学的工具分析了Winkler的解决方案，然后提出了一种性能更好的新策略。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A More Malicious Maitre d’

Abstract In this paper we study the problem of the Malicious Maitre d’, as described in Peter Winkler’s book Mathematical Puzzles: A Connoisseur’s Collection. This problem, attributed to computer scientist Rob Pike, involves seating diners around a circular table with napkins placed between each pair of adjacent settings. The goal of the maitre d’ is to seat the diners in a way that maximizes the number of diners who arrive at the table to find the napkins on both the left and right of their place already taken by their neighbors. Winkler proposes a solution to the problem that he claims is optimal. We analyze Winkler’s solution using tools from enumerative combinatorics, then present a new strategy that performs better.

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来源期刊

American Mathematical Monthly Mathematics-General Mathematics

CiteScore

0.80

自引率

20.00%

发文量

127

审稿时长

6-12 weeks

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