# Waldschmidt constants for Stanley-Reisner ideals of a class of graphs

## TL;DR

This paper investigates Waldschmidt constants for Stanley-Reisner ideals of specific hypergraphs and bipyramid graphs, providing new results and reproofs, revealing series with constants approaching 1.

## Contribution

It introduces new findings on Waldschmidt constants for bipyramid graphs and reestablishes known results for hypergraphs, expanding understanding of these algebraic invariants.

## Key findings

- Waldschmidt constants form descending series approaching 1
- Reproof of Bocci and Franci's main result for hypergraphs
- New results for bipyramid graph Stanley-Reisner ideals

## Abstract

In the present note we study Waldschmidt constants of Stanley-Reisner ideals of a hypergraph and a graph with vertices forming a bipyramid over a planar n-gon. The case of the hypergraph has been studied by Bocci and Franci. We reprove their main result. The case of the graph is new. Interestingly, both cases provide series of ideals with Waldschmidt constants descending to 1. It would be interesting to known if there are bounded ascending sequences of Waldschmidt constants.