The poset of posets

2013/11/09 by Serge Bouc, Bouc, Serge
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Mathematical Theories #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Mathematical Dynamics and Fractals #math.AT #math.CO #math.GR #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1311.2219

arxiv created 2013/11/09 · openalex publication_date 2013/11/09 · arxiv updated 2013/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a finite set. This paper describes some topological and combinatorial properties of the poset Ω_X of order relations on X. In particular, the homotopy type of all the intervals in Ω_X is precisely determined, and the Möbius function of Ω_X is computed.

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