Combinatorics and Commutative Algebra

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Sprache: Englisch

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Beschreibung

Some remarkable connections between commutative algebra and combinatorics have been discovered in recent years. This book provides an overview of two of the main topics in this area. The first concerns the solutions of linear equations in nonnegative integers. Applications are given to the enumeration of integer stochastic matrices (or magic squares), the volume of polytopes, combinatorial reciprocity theorems, and related results. The second topic deals with the face ring of a simplicial complex, and includes a proof of the Upper Bound Conjecture for Spheres. An introductory chapter giving background information in algebra, combinatorics and topology broadens access to this material for non-specialists.

New to this edition is a chapter surveying more recent work related to face rings, focusing on applications to f-vectors.

Über den Autor

Richard P. Stanley is one of the most well-known algebraic combinatorists in the world. He is currently professor of Applied Mathematics at the Massachusetts Institute of Technology. Amongst his several visiting professorships, Stanley has received numerous awards including the George Polya Prize in Applied Combinatorics, Guggenheim Fellowship, admission to both the American Academy and National Academies of Sciences, Leroy P. Steele Prize for Mathematical Exposition, Rolf Schock Prize in Mathematics, Senior Scholar at Clay Mathematics Institute, Aisenstadt Chair, Honorary Doctor of Mathematics from the University of Waterloo, and an honorary professorship at the Nankai University. Professor Stanley has had over 50 doctoral students and is well known for his excellent teaching skills.

Zusammenfassung

The author is well known to the math community as an excellent researcher and expositor in the fields of combinatorics and algebra. His first book was widely read. In this second edition, which contains a significant amount of new material in areas of current interest, Stanley, as before, presents the "big picture" in an engaging framework.

Inhaltsverzeichnis

Background.- Nonnegative Integral Solutions to Linear Equations.- The Face Ring of a Simplicial Complex.- Further Aspects of Face Rings.

Details

Erscheinungsjahr:	2004
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	ix 166 S.
ISBN-13:	9780817643690
ISBN-10:	0817643699
Sprache:	Englisch
Herstellernummer:	11320241
Einband:	Kartoniert / Broschiert
Autor:	Stanley, Richard P.
Auflage:	Second Edition 1996
Hersteller:	Birkhäuser Birkhäuser Boston
Verantwortliche Person für die EU:	Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Maße:	235 x 155 x 11 mm
Von/Mit:	Richard P. Stanley
Erscheinungsdatum:	15.10.2004
Gewicht:	0,283 kg