Linear Equations for the Number of Intervals Which are Isomorphic with Boolean Lattices and the Dehn–Sommerville Equations

DOI10.1080/00927872.2010.517587zbMath1254.06003arXiv1002.2049OpenAlexW2962857984MaRDI QIDQ2902252

Gábor Hegedüs

Publication date: 17 August 2012

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1002.2049

zbMATH Keywords

finite posetfree resolutionscliquesStanley-Reisner ringsDehn-Sommerville equationssimplicial polytopeslattice of order idealsBoolean intervals

Mathematics Subject Classification ID

Combinatorics of partially ordered sets (06A07) Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55) Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69) Algebraic aspects of posets (06A11)

Cites Work

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• Generalized Dehn-Sommerville relations for polytopes, spheres and Eulerian partially ordered sets
• Resolutions of Stanley-Reisner rings and Alexander duality
• Combinatorics and commutative algebra.
• Distributive lattices, bipartite graphs and Alexander duality
• Using Algebraic Geometry
• A Combinatorial Analogue of Poincaré's Duality Theorem
• The monomial ideal of a finite meet-semilattice
• Monomial Ideals Arising From Distributive Lattices