Bjarke Hammersholt Roune
ABSTRACT
We present an algorithm for computing the corners of a monomial ideal. The corners are a set of multidegrees that support the numerical information of a monomial ideal such as Betti numbers and Hilbert-Poincaré series. We show an experiment using corners to compute Hilbert-Poincaré series of monomial ideals with favorable results.
- D. Bayer. Monomial ideals and duality. Never finished draft. See http://www.math.columbia.edu/~bayer/vita.html, 1996.Google Scholar
- D. Bayer and A. Taylor. Reverse search for monomial ideals. Journal of Symbolic Computation, 44:1477--1486, 2009. Google ScholarDigital Library
- A. M. Bigatti. Computation of Hilbert-Poincaré series. Journal of Pure and Applied Algebra, 119(3):237--253, 1997.Google ScholarCross Ref
- A. M. Bigatti, P. Conti, L. Robbiano, and C. Traverso. A "divide and conquer" algorithm for Hilbert-Poincaré series, multiplicity and dimension of monomial ideals. In Applied algebra, algebraic algorithms and error-correcting codes (San Juan, PR, 1993), volume 673 of Lecture Notes in Comput. Sci., pages 76--88. Springer, Berlin, 1993. Google ScholarDigital Library
- A. M. Bigatti and E. S. de Cabezon. (n-1)-st Koszul homology and the structure of monomial ideals. In Proceedings of the 2009 international symposium on Symbolic and algebraic computation, pages 31--38, New York, NY, USA, 2009. ACM. Google ScholarDigital Library
- CoCoATeam. CoCoA: a system for doing Computations in Commutative Algebra. Available at http://cocoa.dima.unige.it.Google Scholar
- E. S. de Cabezon. Combinatorial Koszul homology: Computations and applications, 2008. http://arxiv.org/abs/0803.0421.Google Scholar
- E. Miller and B. Sturmfels. Combinatorial Commutative Algebra, volume 227 of Graduate Texts in Mathematics. Springer, 2005.Google Scholar
- E. Miller, B. Sturmfels, and K. Yanagawa. Generic and cogeneric monomial ideals. Journal of Symbolic Computation, 29(4--5):691--708, 2000. Available at http://www.math.umn.edu/~ezra/papers.html. Google ScholarDigital Library
- B. H. Roune. Frobby version 0.9 -- a software system for computations with monomial ideals. Available at http://www.broune.com/frobby/.Google Scholar
- B. H. Roune. The Slice Algorithm for irreducible decomposition of monomial ideals. Journal of Symbolic Computation, 44(4):358--381, April 2009. Google ScholarDigital Library
- B. H. Roune and E. S. de Cabezon. Combinatorial commutative algebra algorithms for the euler characteristic of abstract simplicial complexes. XII ENCUENTRO DE ÁLGEBRA COMPUTACIONAL Y APLICACIONES (Spanish meeting on Computer Algebra and Applications), 2010.Google Scholar
Index Terms
- A Slice algorithm for corners and Hilbert-Poincaré series of monomial ideals
Recommendations
On the Hilbert series of monomial ideals
To every squarefree monomial ideal one can associate a hypergraph. In this paper we show that the Hilbert series of a squarefree monomial ideal can be obtained from the so-called edge induced polynomial of the associated hypergraph.
Complementary decompositions of monomial ideals and involutive bases
AbstractComplementary decompositions of monomial ideals—also known as Stanley decompositions—play an important role in many places in commutative algebra. In this article, we discuss and compare several algorithms for their computation. This includes a ...
Computing rational powers of monomial ideals
AbstractThis paper concerns fractional powers of monomial ideals. Rational powers of a monomial ideal generalize the integral closure operation as well as recover the family of symbolic powers. They also highlight many interesting connections ...
Comments