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16 papers · 1 filter
The Bergman complex of a matroid and phylogenetic trees
Federico Ardila, Carly Klivans
We study the Bergman complex B(M) of a matroid M: a polyhedral complex which arises in algebraic geometry, but which we describe purely combinatorially. We prove that a natural sub…
Discrete Morse functions from lexicographic orders
Eric Babson, Patricia Hersh
This paper shows how to construct a discrete Morse function with a relatively small number of critical cells for the order complex of any finite poset with and …
Eigenforms of the Laplacian for Riemannian V-submersions
Peter B. Gilkey, Hong-Jong Kim, JeongHyeong Park
Let p: Z -> Y be a Riemannian V-submersion of compact V-manifolds. We study when the pull-back of an eigenform of the Laplacian on Y is an eigenform of the Laplacian on Z, and when…
Subword complexes in Coxeter groups
Allen Knutson, Ezra Miller
Let (Π,Σ) be a Coxeter system. An ordered list of elements in Σand an element in Πdetermine a {\em subword complex}, as introduced in our paper on Gröbner geometry of Schubert poly…
Algorithms for graded injective resolutions and local cohomology over semigroup rings
David Helm, Ezra Miller
Let Q be an affine semigroup generating Z^d, and fix a finitely generated Z^d-graded module M over the semigroup algebra k[Q] for a field k. We provide an algorithm to compute a mi…
Four positive formulae for type A quiver polynomials
Allen Knutson, Ezra Miller, Mark Shimozono
We give four positive formulae for the (equioriented type A) quiver polynomials of Buch and Fulton. All four formulae are combinatorial, in the sense that they are expressed in ter…