Vector partition functions and generalized Dahmen and Micchelli spaces

DOI10.1007/s00031-010-9102-9zbMath1223.58015arXiv0805.2907OpenAlexW2008838943MaRDI QIDQ626569

Corrado De Concini, Michèle Vergne, Claudio Procesi

Publication date: 18 February 2011

Published in: Transformation Groups (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0805.2907

zbMATH Keywords

zonotopelinear Diophantine equationsvector partition functionlocalization formulaquasi-polynomial

Mathematics Subject Classification ID

Special polytopes (linear programming, centrally symmetric, etc.) (52B12) Index theory and related fixed-point theorems on manifolds (58J20) Linear Diophantine equations (11D04) Analytic theory of partitions (11P82) Index theory (19K56)

Related Items

Zonotopal algebra and forward exchange matroids, \([Q,R=0\) and Kostant partition functions], Splines and index theorem, Vector partition functions and index of transversally elliptic operators, Hierarchical zonotopal power ideals, Multiple Bernoulli series, an Euler-Maclaurin formula, and wall crossings, Ehrhart polynomial and arithmetic Tutte polynomial, Wall crossings for double Hurwitz numbers, Infinitesimal index: cohomology computations, The integer cohomology algebra of toric arrangements, Asymptotic equivariant index of Toeplitz operators on the sphere, Geometric realizations and duality for Dahmen-Micchelli modules and De Concini-Procesi-Vergne modules, Quasi-polynomials, linear Diophantine equations and semi-linear sets, The Parikh counting functions of sparse context-free languages are quasi-polynomials, Box splines and the equivariant index theorem, Paradan's wall crossing formula for partition functions and Khovanski-Pukhlikov differential operator, A Tutte polynomial for toric arrangements

Cites Work

• Vector partition functions and index of transversally elliptic operators
• Infinitesimal index: cohomology computations
• A note on the formulars of Guillemin-Kalkman
• Topics in hyperplane arrangements, polytopes and box-splines
• Paradan's wall crossing formula for partition functions and Khovanski-Pukhlikov differential operator
• Residue formulae for vector partitions and Euler-Maclaurin sums.
• On the Solution of Certain Systems of Partial Difference Equations and Linear Dependence of Translates of Box Splines
• The Number of Solutions to Linear Diophantine Equations and Multivariate Splines
• Residue formulae, vector partition functions and lattice points in rational polytopes
• The infinitesimal index
• Localization of the Riemann-Roch character