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arXiv math/9904150math.CO
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赛事Enumeration:问题与进展

Enumeration of Matchings: Problems and Progress

James Propp

摘要:

本文围绕匹配枚举中的32个问题建立,其中前20个问题在1996年秋季MSRI的一次演讲中提出。我首先简要介绍一下配对枚举的历史。二十个原始问题,加上评注,构成了文章的大部分。我介绍了截至撰写本文时在这些问题上取得的进展,并包括印刷和在线文献的指针;最初的二十个问题中大约有一半是由MSRI组合数学研讨会的参与者、他们的学生和其他人解决的。1996年至1999年。文章最后提出了十几个新的未决问题。(Note:本文取代math.CO/9801060和math.CO/9801061。)

英文摘要:

This document is built around a list of thirty-two problems in enumeration of matchings, the first twenty of which were presented in a lecture at MSRI in the fall of 1996. I begin with a capsule history of the topic of enumeration of matchings. The twenty original problems, with commentary, comprise the bulk of the article. I give an account of the progress that has been made on these problems as of this writing, and include pointers to both the printed and on-line literature; roughly half of the original twenty problems were solved by participants in the MSRI Workshop on Combinatorics, their students, and others, between 1996 and 1999. The article concludes with a dozen new open problems. (Note: This article supersedes math.CO/9801060 and math.CO/9801061.)

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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