Higher analogs of simplicial and combinatorial complexity

2019/05/04 by Amit Kumar Paul, Paul, Amit Kumar
Mathematics · #05E45 #55M30 #Algebraic Topology (math.AT) #FOS: Mathematics #Primary: 57Q05 #\ secondary: 06A07 #math.AT #msc:05E45 #msc:06A07 #msc:55M30 #msc:57Q05

paper · pdf · doi:10.48550/arxiv.1905.01440

arxiv created 2019/05/04 · arxiv updated 2019/05/07

Abstract

We introduce higher simplicial complexity of a simplicial complex K and higher combinatorial complexity of a finite space P (i.e. P is a finite poset). We relate higher simplicial complexity with higher topological complexity of |K| and higher combinatorial complexity with higher simplicial complexity of the order complex of P.

Related

• Simplicial and combinatorial versions of higher symmetric topological complexity
• Discrete Topological complexity
• Higher Analogues of Discrete Topological Complexity
• A Finite Equivariant Generalization of Motion Planning and Topological Complexity
• Simplicial Distance