When is there a unique socle-vector associated to a given $h$-vector?
Commutative Algebra
2007-05-23 v2
Abstract
First, we construct a bijection between the set of -vectors and the set of socle-vectors of artinian algebras. As a corollary, we find the minimum codimension that an artinian algebra with a given socle-vector can have. Then, we study the main problem in the paper: determining when there is a unique socle-vector for a given -vector. We solve the problem completely if the codimension is at most 3.
Cite
@article{arxiv.math/0411229,
title = {When is there a unique socle-vector associated to a given $h$-vector?},
author = {Fabrizio Zanello},
journal= {arXiv preprint arXiv:math/0411229},
year = {2007}
}
Comments
21 pages; to appear in Comm. in Algebra