7 papers
Quillen-McCord theorem for persistence finite posets
Vitalii Guzeev, Kohei Tanaka
In this paper, we establish a persistence version of the Quillen-McCord theorem for persistence finite posets. Given a map between persistence finite pos…
Strong homotopy types of acyclic categories and -complexes
Kohei Tanaka
We extend the homotopy theories based on point reduction for finite spaces and simplicial complexes to finite acyclic categories and -complexes, respectively. The functors of cl…
Discrete Morse theory and classifying spaces
Vidit Nanda, Dai Tamaki, Kohei Tanaka
The aim of this paper is to develop a refinement of Forman's discrete Morse theory. To an acyclic partial matching on a finite regular CW complex , Forman introduced a discr…
A combinatorial description of topological complexity for finite spaces
Kohei Tanaka
This paper presents a combinatorial analog of topological complexity for finite spaces. We demonstrate that this coincides with the genuine topological complexity of the original f…
Minimal networks for sensor counting problem using discrete Euler calculus
Kohei Tanaka
This paper proposes a method to reduce noise in acyclic sensor networks enumerating targets using the integral theory with respect to Euler characteristic. For an acyclic network (…
Discrete Euler integration over functions on finite categories
Kohei Tanaka
This paper provides the theory of integration with respect to Euler characteristics of finite categories. As an application, we use sensors to enumerate the targets lying on a pose…