A generalization of a theorem about gapsets with depth at most three

TL;DR

This paper generalizes a theorem about the sequence counting gapsets of genus g with depth at most three, revealing new properties of these combinatorial structures.

Contribution

It extends Eliahou and Fromentin's theorem, providing a broader understanding of gapsets with limited depth and their enumeration.

Findings

New properties of the sequence $(n'_g)$ for gapsets with depth ≤ 3

Generalization of a previous theorem by Eliahou and Fromentin

Enhanced understanding of the structure of gapsets in combinatorics

Abstract

In this paper, we provide a generalization of a theorem proved by Eliahou and Fromentin, which exhibit a remarkable property of the sequence $(n'_g)$, where $n'_g$ denotes the number of gapsets with genus $g$ and depth at most $3$.