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Geometry of the Space of Phylogenetic Trees
We consider a continuous space which models the set of all phylogenetic trees having a fixed set of leaves. This space has a natural metric of nonpositive curvature, giving a way of measuring…
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Generalized Dehn-Sommerville relations for polytopes, spheres and Eulerian partially ordered sets
This paper generalizes the Dehn-Sommerville equations for simplicial spheres to related classes of objects. The underlying motivation is to understand the combinatorial structure of arbitrary…
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Decompositions of Simplicial Complexes Related to Diameters of Convex Polyhedra
TLDR
It is shown that several cases in which the Hirsch conjecture has been verified can be handled by these methods, which also give the shellability of a number of simplicial complexes of combinatorial interest.
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Homology of smooth splines: generic triangulations and a conjecture of Strang
For A a triangulated d-dimensional region in Rd, let Sr (A) denote the vector space of all cr functions F on A that, restricted to any simplex in A, are given by polynomials of degree at most m. We…
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A Proof of the Sufficiency of McMullen's Conditions for f-Vectors of Simplicial Convex Polytopes
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A quasisymmetric function for matroids
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Allocation of Shared Costs: A Set of Axioms Yielding A Unique Procedure
TLDR
In this note, cost allocation procedures are considered and it is shown that there is exactly one such procedure which possesses four desirable properties.
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On games without side payments arising from a general class of markets
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Constructions and complexity of secondary polytopes
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Sufficiency of McMullen's conditions for $f$-vectors of simplicial polytopes
For convex d-polytope P let ft{P) equal the number of faces of P of dimension i, 0 < i < d 1. f(P) = (f0(P)9 . . . , fd^QP)) is called the f vector of P An important combinatorial problem is the…
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