Derangement Frequency in the Boolean Complex
Kari Ragnarsson, Bridget Eileen Tenner
TL;DR
This paper investigates how often specific derangements of vertices occur within the Boolean complex of a graph, linking combinatorial derangements to topological structures.
Contribution
It introduces a study of derangement frequencies in the Boolean complex, connecting combinatorial derangements with the homotopy type of the complex.
Findings
Identifies the frequency distribution of derangements in the Boolean complex
Establishes a bijection between derangements and spheres in the homotopy type
Provides insights into the combinatorial structure of the Boolean complex
Abstract
In previous work, we associated to any finite simple graph a particular set of derangements of its vertices. These derangements are in bijection with the spheres in the wedge sum describing the homotopy type of the boolean complex for this graph. Here we study the frequency with which a given derangement appears in this set.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Advanced Combinatorial Mathematics · Alzheimer's disease research and treatments