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Semi-algebraic sets of f-vectors
Hannah Sjöberg, Günter M. Ziegler
Polytope theory has produced a great number of remarkably simple and complete characterization results for face-number sets or f-vector sets of classes of polytopes. We observe tha…
Additive structures on -vector sets of polytopes
Günter M. Ziegler
We show that the -vector sets of -polytopes have non-trivial additive structure: They span affine lattices and are embedded in monoids that we describe explicitly. Moreover,…
Simple polytopes without small separators, II: Thurston's bound
Lauri Loiskekoski, Günter M. Ziegler
We show that there are simple 4-dimensional polytopes with n vertices such that all separators of the graph have size at least . This establishes a strong form of a cl…
Area difference bounds for dissections of a square into an odd number of triangles
Jean-Philippe Labbé, Günter Rote, Günter M. Ziegler
Monsky's theorem from 1970 states that a square cannot be dissected into an odd number of triangles of the same area, but it does not give a lower bound for the area differences th…