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- Nicole Berline, E. Getzler
- 1995
Perhaps the most famous theorem of the 1960’s, the Atiyah-Singer index theorem bears all the hallmarks of great mathematics: it draws on and relates several fields in mathematics, explicating and… (More)
- Velleda Baldoni, Nicole Berline, Jesús A. De Loera, Matthias Köppe, Michèle Vergne
- Math. Comput.
- 2011
This paper settles the computational complexity of the problem of integrating a polynomial function f over a rational simplex. We prove that the problem is NP-hard for arbitrary polynomials via a… (More)
- Velleda Baldoni, Nicole Berline, Jesús A. De Loera, Matthias Köppe, Michèle Vergne
- Foundations of Computational Mathematics
- 2012
This article concerns the computational problem of counting the lattice points inside convex polytopes, when each point must be counted with a weight associated to it. We describe an efficient… (More)
where b(n) are the Bernoulli numbers. When p is an integral polytope, the existence of such operators is the combinatorial counterpart of a homological property of the associated toric variety: the… (More)
- Velleda Baldoni, Nicole Berline, Matthias Köppe, Michèle Vergne
- ArXiv
- 2010
We study intermediate sums, interpolating between integrals and discrete sums, which were introduced by A. Barvinok [Computing the Ehrhart quasi-polynomial of a rational simplex, Math. Comp. 75… (More)
Velleda Baldoni, Nicole Berline, Michèle Vergne. Local Euler-Maclaurin expansion of Barvinok valuations and Ehrhart coefficients of a rational polytope. Matthias Beck, Christian Haase, Bruce Reznick,… (More)
- Nicole Berline, Jesús A. De Loera, B. E. DUTRA, Matthias Köppe, Michèle Vergne
- 2014
For a given sequence α = [α1, α2, . . . , αN+1] of N + 1 positive integers, we consider the combinatorial function E(α)(t) that counts the non-negative integer solutions of the equation α1x1 +α2x2 +… (More)
We write the equivariant Todd class of a general complete toric variety as an explicit combination of the orbit closures, the coefficients being analytic functions on the Lie algebra of the torus… (More)