A new face iterator for polyhedra and for more general finite locally branched lattices

DOI10.1007/s00454-021-00344-xzbMath1489.52010arXiv1905.01945OpenAlexW4221073203MaRDI QIDQ2136840

Christian Stump, Jonathan Kliem

Publication date: 16 May 2022

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.01945

zbMATH Keywords

polyhedron\(f\)-vectorenumerationnumerical semigroupface latticeWilf's conjectureface iteratormemory-efficient depth-first algorithm

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Exact enumeration problems, generating functions (05A15) Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Commutative semigroups (20M14) Combinatorics of partially ordered sets (06A07) Combinatorial aspects of matroids and geometric lattices (05B35) Computational methods for problems pertaining to group theory (20-08)

Uses Software

• Normaliz
• polymake
• CRoaring

Cites Work

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• Generalizations of Eulerian partially ordered sets, flag numbers, and the Möbius function
• Computing the face lattice of a polytope from its vertex-facet incidences
• Algorithms for tight spans and tropical linear spaces
• A graph-theoretic approach to Wilf's conjecture
• Wilf’s conjecture in fixed multiplicity
• Lectures on Polytopes