|
Vertex cover algebras of unimodular hypergraphs
Author(s):
Jürgen
Herzog;
Takayuki
Hibi;
Ngô
Viêt
Trung
Journal:
Proc. Amer. Math. Soc.
137
(2009),
409-414.
MSC (2000):
Primary 13D02, 05C65
Posted:
October 9, 2008
MathSciNet review:
2448558
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
It is proved that all vertex cover algebras of a hypergraph are standard graded if and only if the hypergraph is unimodular. This has interesting consequences on the symbolic powers of monomial ideals.
References:
-
- 1.
- C. Berge, Hypergraphs. Combinatorics of finite sets, North-Holland, 1989. MR 1013569 (90h:05090)
- 2.
- C.A. Escobar, R. Villarreal and Y. Yoshino, Torsion freeness and normality of blowup rings of monomial ideals. Commutative algebra, 69-84, Lect. Notes Pure Appl. Math. 244, Chapman & Hall/CRC, 2006. MR 2184791 (2007c:13005)
- 3.
- I. Gitler, C.E. Valencia and R. Villarreal, A note on Rees algebras and the MFMC property, Beiträge Algebra Geom. 48 (2007), No. 1, 141-150. MR 2326406 (2008f:13004)
- 4.
- J. Herzog, T. Hibi and N.V. Trung, Symbolic powers of monomial ideals and vertex cover algebras, Adv. Math. 210 (2007), 304-322. MR 2298826 (2007m:13005)
- 5.
- J. Herzog, T. Hibi, N.V. Trung and X. Zheng, Standard graded vertex cover algebras, cycles and leaves, Trans. Amer. Math. Soc. 360 (2008), No. 12, 6231-6249.
- 6.
- A. Schrijver, Theory of linear and integer programming, Wiley, 1998. MR 874114 (88m:90090)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2000):
13D02, 05C65
Retrieve articles in all Journals with
MSC (2000):
13D02, 05C65
Additional Information:
Jürgen
Herzog
Affiliation:
Fachbereich Mathematik und Informatik, Universität Duisburg-Essen, Campus Essen, 45117 Essen, Germany
Email:
juergen.herzog@uni-essen.de
Takayuki
Hibi
Affiliation:
Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Toyonaka, Osaka 560-0043, Japan
Email:
hibi@math.sci.osaka-u.ac.jp
Ngô
Viêt
Trung
Affiliation:
Institute of Mathematics, Vien Toan Hoc, 18 Hoang Quoc Viet, 10307 Hanoi, Vietnam
Email:
nvtrung@math.ac.vn
DOI:
10.1090/S0002-9939-08-09308-8
PII:
S 0002-9939(08)09308-8
Keywords:
Vertex cover algebra,
unimodular hypergraph,
symbolic power,
monomial ideal
Received by editor(s):
March 18, 2007
Posted:
October 9, 2008
Communicated by:
Bernd Ulrich
Copyright of article:
Copyright
2008,
American Mathematical Society
|
