Sequences defined by h-vectors

TL;DR

This paper investigates the sequence of counts of h-vectors of length n, establishing bounds related to Fibonacci numbers and integer partitions, and explores related embedded sequences.

Contribution

It introduces bounds for the sequence of h-vector counts using Fibonacci numbers and integer partitions, and studies related embedded sequences.

Findings

The sequence's nth term is bounded above by Fibonacci numbers.

The sequence's nth term is bounded below by the number of partitions into distinct parts.

Embedded sequences related to integer partitions are identified.

Abstract

In this paper we consider the sequence whose n^{th} term is the number of h-vectors of length n. We show that the n^{th} term of this sequence is bounded above by the n^{th} Fibonacci number and bounded below by the number if integer partitions of n into distinct parts. Further we show embedded sequences that directly relate to integer partitions.