On the combinatorics of Murai spheres and its applications
Ivan Limonchenko, Ale\v{s} Vavpeti\v{c}

TL;DR
This paper classifies Murai spheres in low dimensions, explores their convex realizations, describes specific chordal cases, and determines key combinatorial invariants like Buchstaber and chromatic numbers.
Contribution
It provides a complete classification of Murai spheres in dimensions 1 and 2, including their convex realizations and combinatorial invariants, advancing understanding of their structure.
Findings
Murai spheres in dimensions 1 and 2 are classified.
Convex simple polytopes associated with these spheres have Delzant realizations.
All possible Buchstaber and chromatic numbers for Murai spheres are determined.
Abstract
We classify the combinatorial types of Murai spheres in dimensions and , thereby showing that the corresponding convex simple polytopes have Delzant realizations. Then we describe all chordal Murai spheres with and . Finally, we find all possible values for the Buchstaber and chromatic numbers of arbitrary Murai spheres.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Topological and Geometric Data Analysis · Commutative Algebra and Its Applications
