Quotients of Peck posets

DOI10.1007/BF00396271zbMath0564.06002WikidataQ29307715 ScholiaQ29307715MaRDI QIDQ1057888

Richard P. Stanley

Publication date: 1984

Published in: Order (Search for Journal in Brave)

zbMATH Keywords

Sperner propertyfinite group of automorphismsedge-reconstruction conjectureunitary Peck posets

Mathematics Subject Classification ID

Partial orders, general (06A06) Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) (05C60)

Related Items

Reconstructing graphs from their k-edge deleted subgraphs ⋮ The first higher Stasheff-Tamari orders are quotients of the higher Bruhat orders ⋮ Finite-type invariants for graphs and graph reconstructions ⋮ A Dynkin diagram classification theorem arising from a combinatorial problem ⋮ Problems on chain partitions ⋮ On posets of \(m\)-ary words ⋮ Peckness of edge posets ⋮ Order polynomials and Pólya's enumeration theorem. ⋮ Dominance order on signed integer partitions ⋮ Double posets and the antipode of QSym ⋮ Action on Grassmannians Associated with a Field Extension ⋮ Action on Grassmannians Associated with Commutative Semisimple Algebras ⋮ Symmetric chain decompositions of products of posets with long chains ⋮ The \(k\)-orbit reconstruction and the orbit algebra ⋮ The necklace poset is a symmetric chain order ⋮ Product evaluations of Lefschetz determinants for Grassmannians and of determinants of multinomial coefficients ⋮ On quotients of posets, with an application to the \(q\)-analog of the hypercube ⋮ Differential Posets ⋮ On the existence of symmetric chain decompositions in a quotient of the Boolean lattice ⋮ Reconstruction from vertex-switching ⋮ Solution of a Sperner conjecture of Stanley with a construction of Gelfand ⋮ Symmetric chain decompositions of quotients by wreath products.

Cites Work

• Unnamed Item
• Product partial orders with the Sperner property
• Some aspects of groups acting on finite posets
• Application d'une propriété combinatoire des parties d'un ensemble aux groupes et aux rélations
• The edge reconstruction hypothesis is true for graphs with more than n log n edges
• Sperner properties for groups and relations
• On incidence matrices of finite projective and affine spaces
• A note on the line reconstruction problem
• Morphisms for the strong Sperner property of Stanley and Griggs
• A sperner property preserved by product
• Weyl Groups, the Hard Lefschetz Theorem, and the Sperner Property
• Graph reconstruction—a survey
• Solution of Two Difficult Combinatorial Problems with Linear Algebra