Description
Book SynopsisThis book demonstrates current trends in research on combinatorial and computational commutative algebra with a primary emphasis on topics related to monomial ideals.
Providing a useful and quick introduction to areas of research spanning these fields, Monomial Ideals is split into three parts.
Trade ReviewFrom the reviews:
“The authors … who themselves have played an important, often crucial, role in recent developments of the subject, make an ideal co-author pairing for composing a book with such a comprehensive choice of material, including the latest achievements. It should serve as a useful resource for researchers in both commutative algebra and combinatorics. … The presentation of the material is distinctive for its clarity and elegant style. … The text can serve nicely as a basis for a couple of graduate courses in two semesters.” (Rahim Zaare-Nahandi, Mathematical Reviews, Issue 2011 k)
Table of ContentsPart I Gröbner bases: Monomial Ideals.- A short introduction to Gröbner bases.- Monomial orders and weights.- Generic initial ideals.- The exterior algebra.- Part II: Hilbert functions and resolutions.- Hilbert functions and the theorems of Macaulay and Kruskal-Katona.- Resolutions of monomial ideals and the Eliahou-Kervaire formula.- Alexander duality and resolutions.- Part III Combinatorics: Alexander duality and finite graphs.- Powers of monomial ideals.- Shifting theory.- Discrete Polymatroids.- Some homological algebra.- Geometry
