A note on the asymptotics of the number of O-sequences of given length
Department of Mathematical Sciences
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.
A note on the asymptotics of the number of O-sequences of given length.
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©2019 Elsevier B.V. All rights reserved. Publisher’s version of record: https://doi.org/10.1016/j.disc.2019.04.001