Convex Geometries yielded by Transit Functions

2024/06/03 by Manoj Changat, Changat, Manoj, Lekshmi Kamal K. Sheela +5
Mathematics · #05C38 #52A01 #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2406.01100

openalex publication_date 2024/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let V be a finite nonempty set. A transit function is a map R:V× V→ 2^V such that R(u,u)=\u\, R(u,v)=R(v,u) and u∈ R(u,v) hold for every u,v∈ V. A set K⊆ V is R-convex if R(u,v)⊂ K for every u,v∈ K and all R-convex subsets of V form a convexity C_R. We consider Minkowski-Krein-Milman property that every R-convex set K in a convexity C_R is the convex hull of the set of extreme points of K from axiomatic point of view and present a characterization of it. Later we consider several well-known transit functions on graphs and present the use of the mentioned characterizations on them.

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