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A Beginner’s Guide to Edge and Cover Ideals
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A Beginner’s Guide to Edge and Cover Ideals

Abstract

Monomial ideals, although intrinsically interesting, play an important role in studying the connections between commutative algebra and combinatorics. Broadly speaking, problems in combinatorics are encoded into monomial ideals, which then allow us to use techniques and methods in commutative algebra to solve the original question. Stanley’s proof of the Upper Bound Conjecture [180] for simplicial spheres is seen as one of the early highlights of exploiting this connection between two fields. To bridge these two areas of mathematics, Stanley used square-free monomial ideals.

Authors

Van Tuyl A

Series

Lecture Notes in Mathematics

Volume

2083

Pagination

pp. 63-94

Publisher

Springer Nature

Publication Date

January 1, 2013

DOI

10.1007/978-3-642-38742-5_3

Conference proceedings

Lecture Notes in Mathematics

ISSN

0075-8434

Labels

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