Computation of Poincaré-Betti Series for Monomial Rings
نویسنده
چکیده
The multigraded Poincaré-Betti series P k R(x̄; t) of a monomial ring k[x̄]/〈M〉 on a finite number of monomial generators has the form ∏ xi∈x̄ (1+xit)/bR,k(x̄; t), where bR,k(x̄; t) is a polynomial depending only on the monomial set M and the characteristic of the field k. I present a computer program designed to calculate the polynomial bR,k for a given field characteristic and a given set of monomial generators.
منابع مشابه
New Algorithm For Computing Secondary Invariants of Invariant Rings of Monomial Groups
In this paper, a new algorithm for computing secondary invariants of invariant rings of monomial groups is presented. The main idea is to compute simultaneously a truncated SAGBI-G basis and the standard invariants of the ideal generated by the set of primary invariants. The advantage of the presented algorithm lies in the fact that it is well-suited to complexity analysis and very easy to i...
متن کاملSegre Embeddings, Hilbert Series and Newcomb’s Problem
Monomial ideals and toric rings are closely related. By consider a Grobner basis we can always associated to any ideal I in a polynomial ring a monomial ideal in≺I, in some special situations the monomial ideal in≺I is square free. On the other hand given any monomial ideal I of a polynomial ring S, we can define the toric K[I] ⊂ S. In this paper we will study toric rings defined by Segre embed...
متن کاملOn the Denominator of the Poincaré Series for Monomial Quotient Rings
Let S = k[x1, . . . , xn] be a polynomial ring over a field k and I a monomial ideal of S. It is well known that the Poincaré series of k over S/I is rational. We describe the coefficients of the denominator of the series and study the multigraded homotopy Lie algebra of S/I.
متن کاملPoincaré Series of Monomial Rings
Let k be a field, let I be an ideal generated by monomials in the polynomial ring k[x1, . . . , xt] and let R = k[x1, . . . , xt]/I be the associated monomial ring. The k-vector spaces Tori (k, k) are N -graded. We derive a formula for the multigraded Poincaré series of R, PRk (x, z) = ∑ i≥0,α∈Nt dimk Tor R i,α(k, k)x z, in terms of the homology of certain simplicial complexes associated to sub...
متن کاملAlexander Duality for Monomial Ideals and Their Resolutions
Alexander duality has, in the past, made its way into commutative algebra through Stanley-Reisner rings of simplicial complexes. This has the disadvantage that one is limited to squarefree monomial ideals. The notion of Alexander duality is generalized here to arbitrary monomial ideals. It is shown how this duality is naturally expressed by Bass numbers, in their relations to the Betti numbers ...
متن کامل