Work

Strong Greedoid Structure of $r$-Removed $P$-Orderings

Year: 2024

Type: article

Abstract: Inspired by the notion of $r$-removed $P$-orderings introduced in the setting of Dedekind domains by Bhargava, we generalize it to the framework of arbitrary ultrametric spaces. We show that sets of maximal "$r$-removed perimeter" can be constructed by a greedy algorithm and form a strong greedoid. This gives a simplified proof of several theorems previously obtained by Bhargava, as well as generalises some results of Grinberg and Petrov who considered the case $r=0$ corresponding, in turn, to simple $P$-orderings.

Source: The Electronic Journal of Combinatorics

DOI: 10.37236/12403

Authors: Dmitrii Krachun, Rozalina Mirgalimova

Institutions: Princeton University, St Petersburg University

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Russian Science Foundation

Award: G7433081268