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A wealth of geometric and combinatorial properties of a given linear endomorphism $X$ of $\R^N$ is captured in the study of its associated zonotope $Z(X)$, and, by duality, its associated hyperplane arrangement ${\cal H}(X)$.
Products of linear forms and Tutte polynomials
Berget, A · 1935
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Analyse spectrale sur Z n Z_{n}
Lefranc, M · 1953
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On zonotopes
McMullen, P · 1971
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Commutative rings
Kaplansky, I · 1974
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Combinatorial properties of associated zonotopes
Shephard, G. C · 1974
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Space-filling zonotopes
Shephard, G. C · 1974
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Space tiling zonotopes
McMullen, P · 1975
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B B -splines from parallelepipeds
de Boor, C., and Höllig, K · 1982
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Translates of multivariate splines
Dahmen, W., and Micchelli, C. A · 1983
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On the local linear independence of translates of a box spline
Dahmen, W., and Micchelli, C. A · 1985
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On the solution of certain systems of partial difference equations and linear dependence of translates of box splines
Dahmen, W., and Micchelli, C. A · 1985
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A system of differential equations that is related to the polynomial class of translates of a box spline
Akopyan, A. A., and Saakyan, A. A · 1988
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Translates of exponential box splines and their related spaces
Ben-Artzi, A., and Ron, A · 1988
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Exponential box splines
Ron, A · 1988
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A class of systems of partial differential equations
Akopyan, A. A., and Saakyan, A. A · 1989
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On multivariate E E -splines
Dahmen, W., and Micchelli, C. A · 1989
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Local dimension of piecewise polynomial spaces, syzygies, and solutions of systems of partial differential equations
Dahmen, W., and Micchelli, C. A · 1990
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On multivariate polynomial interpolation
de Boor, C., and Ron, A · 1990
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Local approximation by certain spaces of exponential polynomials, approximation order of exponential box splines, and related interpolation problems
Dyn, N., and Ron, A · 1990
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On multivariate polynomial interpolation
Dyn, N., and Ron, A · 1990
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On two polynomial spaces associated with a box spline
de Boor, C., Dyn, N., and Ron, A · 1991
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On polynomial ideals of finite codimension with applications to box spline theory
de Boor, C., and Ron, A · 1991
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A zonotope associated with graphical degree sequences
Stanley, R. P · 1991
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Computational aspects of polynomial interpolation in several variables
de Boor, C., and Ron, A · 1992
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The least solution for the polynomial interpolation problem
de Boor, C., and Ron, A · 1992
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Matroid theory
Oxley, J. G · 1992
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Multidimensional splines and polynomial interpolation
Akopyan, A. A., and Saakyan, A. A · 1993
Cited alongside, same era.
Algebraic graph theory
Biggs, N · 1993
Cited alongside, same era.
Box splines
de Boor, C., Höllig, K., and Riemenschneider, S · 1993
Coefficients and roots of Ehrhart polynomials
Beck, M., De Loera, J. A., Develin, M., Pfeifle, J., and Stanley, R. P · 2005
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Abelianization for hyperkähler quotients
Hausel, T., and Proudfoot, N · 2005
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The algebra of the box spline
De Concini, C., and Procesi, C · 2006
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Intersection forms of toric hyperkähler varieties
Hausel, T., and Swartz, E · 2006
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An introduction to hyperplane arrangements, 2004–2006
Stanley, R. P · 2006
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Computing the continuous discretely
Beck, M., and Robins, S · 2007
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Hyperplane arrangements and box splines
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Commutative algebras for arrangements
Orlik, P., and Terao, H · 1994
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Zonotopal tilings and the Bohne-Dress theorem
Richter-Gebert, J., and Ziegler, G. M · 1994
Cited alongside, same era.
Commutative algebra
Eisenbud, D · 1995
Cited alongside, same era.
Lectures on polytopes
Ziegler, G. M · 1995
Cited alongside, same era.
On multivariate splines, matroids, and the Ext-functor
Dahmen, W., Dress, A., and Micchelli, C. A · 1996
Cited alongside, same era.
De Concini, C., and Procesi, C · 2008
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Vector partition function and generalized Dahmen-Micchelli spaces
De Concini, C., Procesi, C., and Vergne, M · 2008
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Vector partition functions and index of transversally elliptic operators
De Concini, C., Procesi, C. C., and Vergne, M · 2008
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Multiparking functions, graph searching, and the Tutte polynomial
Kostić, D., and Yan, C. H · 2008
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Hierarchical zonotopal spaces
Holtz, O., Ron, A., and Xu, Z · 2009
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A Tutte polynomial for toric arrangements
Moci, L · 2009
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Private communication, Nov. 2010
Ardila, F · 2010
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Combinatorics and geometry of power ideals
Ardila, F., and Postnikov, A · 2010
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Box splines and the equivariant index theorem
De Concini, C., Procesi, C., and Vergne, M · 2010
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Monomization of Power Ideals and Parking Functions
Desjardins, C · 2010
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Hierarchical zonotopal power ideals
Lenz, M · 2010
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Sagbi bases of Cox-Nagata rings
Sturmfels, B., and Xu, Z · 2010
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Ehrhart polynomial and multiplicity Tutte polynomial
D’Adderio, M., and Moci, L · 2011
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Topics in hyperplane arrangements, polytopes and box-splines
De Concini, C., and Procesi, C · 2011
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Zonotopal combinatorics, 2011
Holtz, O., and Ron, A · 2011
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