On the cardinalities of finite topologies and the number of antichains in partially ordered sets

DOI10.1016/0012-365X(81)90202-8zbMath0465.05009MaRDI QIDQ1154468

Marcel Erné

Publication date: 1981

Published in: Discrete Mathematics (Search for Journal in Brave)

Mathematics Subject Classification ID

Partial orders, general (06A06) Combinatorial identities, bijective combinatorics (05A19) Lower separation axioms ((T_0)--(T_3), etc.) (54D10)

Related Items (10)

Chains in lattices of mappings and finite fuzzy topological spaces ⋮ New results from an algorithm for counting posets ⋮ Counting finite posets and topologies ⋮ Riordan posets and associated incidence matrices ⋮ Obtainable sizes of topologies on finite sets ⋮ Unnamed Item ⋮ Some recurrence relations in finite topologies ⋮ A framework for the systematic determination of the posets on \(n\) points with at least \(\tau \cdot 2^n\) downsets ⋮ A generalization of a theorem of Erné about the number of posets with a fixed antichain ⋮ On the number of reachable pairs in a digraph

Cites Work

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• On the cardinalities of finite topologies
• On the number of open sets of finite topologies
• Struktur- und Anzahlformeln für Topologien auf endlichen Mengen
• A Machine Representation of Finite T ₀ Topologies
• Asymptotic Enumeration of Partial Orders on a Finite Set
• Quasi-Orderings and Topologies on Finite Sets
• On the computer enumeration of finite topologies

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