Simplicial and combinatorial versions of higher symmetric topological complexity

In this paper, we introduce higher symmetric simplicial complexity SCnΣ(K) of a simplicial complex K and higher symmetric combinatorial complexity CCnΣ(P) of a finite poset P. These are simplicial and combinatorial approaches to symmetric motion planning of Basabe - González - Rudyak - Tamaki. We pr...

Full description

Saved in:
Bibliographic Details
Published in:Topology and its applications 2023-05, Vol.331, p.108491, Article 108491
Main Authors: Paul, Amit Kumar, Sen, Debasis
Format: Article
Language:English
Subjects:
Finite space
Simplicial complex
Symmetric group
Topological complexity
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we introduce higher symmetric simplicial complexity SCnΣ(K) of a simplicial complex K and higher symmetric combinatorial complexity CCnΣ(P) of a finite poset P. These are simplicial and combinatorial approaches to symmetric motion planning of Basabe - González - Rudyak - Tamaki. We prove that the symmetric simplicial complexity SCnΣ(K) is equal to symmetric topological complexity TCnΣ(|K|) of the geometric realization of K and the symmetric combinatorial complexity CCnΣ(P) is equal to symmetric topological complexity TCnΣ(|K(P)|) of the geometric realization of the order complex of P.
ISSN:0166-8641
DOI:10.1016/j.topol.2023.108491