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A special class of pure $O$-sequences

Tài Huy Hà, Takayuki Hibi, Fabrizio Zanello

Abstract

The pure $O$-sequences of the form $(1,a,a,\ldots)$ are classified.

A special class of pure $O$-sequences

Abstract

The pure -sequences of the form are classified.
Paper Structure (2 sections, 5 theorems, 7 equations)

This paper contains 2 sections, 5 theorems, 7 equations.

Table of Contents

  1. Proof of Theorem \ref{['New_Orleans']}
  2. The pure $O$-sequences $(1,a,b)$ and $(1,a,a,b)$

Key Result

Theorem A

Let $n \geq 4$. Then a sequence $h=(1,a,a,\ldots,a,b) \in {\mathbb Z}_{>0}^{n+1}$ is a pure $O$-sequence if and only if $b \leq a \leq 2b$.

Theorems & Definitions (13)

  • Theorem A
  • Lemma 1.1
  • proof
  • Lemma 1.2
  • proof
  • Lemma 1.3
  • proof
  • Remark 1.4
  • Remark 1.5
  • Remark 1.6
  • ...and 3 more