152 citations · 375 across the 47 of their papers we have counts for
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Cohomology of GKM Fiber Bundles
Victor Guillemin, Silvia Sabatini, Catalin Zara
The equivariant cohomology ring of a GKM manifold is isomorphic to the cohomology ring of its GKM graph. In this paper we explore the implications of this fact for equivariant fibe…
Riemann sums over polytopes
Victor Guillemin, Shlomo Sternberg
We show that the Euler-MacLaurin formula for Riemann sums has an n-dimensional analogue in which intervals on the line get replaced by convex polytopes.
The Ehrhart Function for Symbols
Victor W. Guillemin, Shlomo Sternberg, Jonathan Weitsman
We derive an Ehrhart function for symbols from the Euler-MacLaurin formula with remainder.
Signature quantization, representations of compact Lie groups, and a q-analogue of the Kostant partition function
Victor Guillemin, Etienne Rassart
We discuss some applications of signature quantization to the representation theory of compact Lie groups. In particular, we prove signature analogues of the Kostant formula for we…
A vector partition function for the multiplicities of sl_k(C)
Sara Billey, Victor Guillemin, Etienne Rassart
We use Gelfand-Tsetlin diagrams to write down the weight multiplicity function for the Lie algebra sl_k(C) (type A_{k-1}) as a single partition function. This allows us to apply kn…
How is a graph like a manifold?
Ethan Bolker, Victor Guillemin, Tara Holm
In this article, we discuss some classical problems in combinatorics which can be solved by exploiting analogues between graph theory and the theory of manifolds. One well-known ex…