A note on the asymptotics of the number of O-sequences of given length

Authors

Richard Stanley, MIT
Fabrizio Zanello, Michigan Technological UniversityFollow

Document Type

Article

Publication Date

7-2019

Department

Department of Mathematical Sciences

Abstract

We look at the number L(n) of O-sequences of length n. Recall that an O-sequence can be defined algebraically as the Hilbert function of a standard graded k-algebra,or combinatorially as the f-vector of a multicomplex. The sequence L(n) was first investigated in a recent paper by commutative algebraists Enkosky and Stone, inspired by Huneke. In this note, we significantly improve both of their upper and lower bounds, by means of a very short partition-theoretic argument.

Publisher's Statement

©2019 Elsevier B.V. All rights reserved. Publisher’s version of record: https://doi.org/10.1016/j.disc.2019.04.001

Publication Title

Discrete Mathematics

Recommended Citation

Stanley, R., & Zanello, F. (2019). A note on the asymptotics of the number of O-sequences of given length. Discrete Mathematics, 342(7), 2033-2034. http://doi.org/10.1016/j.disc.2019.04.001
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/222