English

Enumeration of concave integer partitions

Combinatorics 2007-05-23 v5 Commutative Algebra

Abstract

An integer partition \lambda of n corresponds, via its Ferrers diagram, to an artinian monomial ideal I of colength n in the polynomial ring on two variables. If the partition \lambda corresponds to an integrally closed ideal we call \lambda concave. We study generating functions for the number of concave partitions, unrestricted or with at most r parts.

Keywords

Cite

@article{arxiv.math/0309065,
  title  = {Enumeration of concave integer partitions},
  author = {Jan Snellman and Michael Paulsen},
  journal= {arXiv preprint arXiv:math/0309065},
  year   = {2007}
}

Comments

8 pages. ver 2: Added reference to asymptotic estimate by Gert Almkvist. ver 3: Minor editing. ver 4: Added reference to Canfield et al, rewrote section 3 ver 5: Added reference to Andrews