Counting finite posets and topologies

DOI10.1007/BF00383446zbMath0752.05002OpenAlexW2006026808MaRDI QIDQ1183945

Marcel Erné, Kurt Stege

Publication date: 28 June 1992

Published in: Order (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00383446

zbMATH Keywords

partially ordered setsfinite topological spacesquasiordered sets

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial identities, bijective combinatorics (05A19) Combinatorics of partially ordered sets (06A07) Cardinality properties (cardinal functions and inequalities, discrete subsets) (54A25) Lower separation axioms ((T_0)--(T_3), etc.) (54D10)

Related Items (34)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
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• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Dénombrement des ordres étagés
• The number of tiered posets modulo six
• Counting unlabeled structures
• Counting interval orders
• Asymptotic enumeration of two-dimensional posets
• An asymptotic equivalent for the number of total preorders on a finite set
• On the cardinalities of finite topologies and the number of antichains in partially ordered sets
• Enumeration of generalized weak orders
• New results from an algorithm for counting posets
• Counting finite posets and topologies
• The number of partially ordered sets with more points than incomparable pairs
• On the cardinalities of finite topologies
• Asymptotic enumeration on partially ordered sets
• On the number of open sets of finite topologies
• The number of partially ordered sets
• The lattice of natural partial orders
• On the enumeration of finite maximal connected topologies
• Struktur- und Anzahlformeln für Topologien auf endlichen Mengen
• A Machine Representation of Finite T ₀ Topologies
• A solution of Dedekind's problem on the number of isotone Boolean functions.
• The Asymptotic Number of Lattices
• Enumeration of Posets Generated by Disjoint Unions and Ordinal Sums
• Counting of finite topologies and a dissection of Stirling numbers of the second kind
• Asymptotic Enumeration of Partial Orders on a Finite Set
• Entropy and phase transitions in partially ordered sets
• Counting finite posets
• On the Number of Topologies on A Finite Set
• Finite Topological Spaces
• Quasi-Orderings and Topologies on Finite Sets
• On the number of topologies definable for a finite set
• Cardinality of finite topologies
• On the computer enumeration of finite topologies
• Note on Finite Topological Spaces
• The number of graded partially ordered sets
• Natural Partial Orders
• Topology on Finite Sets
• The Number of Finite Topologies
• Endliche Verbände.
• On the Structure of Finite T₀ + T₅ Spaces

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