Results 41 to 50 of about 2,436 (140)
Belt distance between facets of space-filling zonotopes [PDF]
, 2010 For every d-dimensional polytope P with centrally symmetric facets we can associate a "subway map" such that every line of this "subway" corresponds to set of facets parallel to one of ridges P.
Garber, Alexey
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Hierarchical zonotopal power ideals [PDF]
European Journal of Combinatorics, 2011 Zonotopal algebra deals with ideals and vector spaces of polynomials that are related to several combinatorial and geometric structures defined by a finite sequence of vectors. Given such a sequence $X$, an integer $k \geq -1$ and an upper set in the lattice of flats of the matroid defined by $X$, we define and study the associated $\textit ...
openaire +5 more sources
Description of the symmetric convex random closed sets as zonotopes from their Feret diameters
Modern Stochastics: Theory and Applications, 2017 In this paper, the 2-D random closed sets (RACS) are studied by means of the Feret diameter, also known as the caliper diameter. More specifically, it is shown that a 2-D symmetric convex RACS can be approximated as precisely as we want by some random ...
Saïd Rahmani +2 more
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Observadores Distribuidos Garantistas para Sistemas en Red
Revista Iberoamericana de Automática e Informática Industrial RIAI, 2017 Resumen: En este artículo se propone un observador distribuido garantista para sistemas en red, considerando de forma explícita el problema de los retardos variables en las comunicaciones.
Ramón A. García +4 more
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A probabilistic interpretation of set-membership filtering: application to polynomial systems through polytopic bounding [PDF]
, 2016 Set-membership estimation is usually formulated in the context of set-valued calculus and no probabilistic calculations are necessary. In this paper, we show that set-membership estimation can be equivalently formulated in the probabilistic setting by ...
Benavoli, Alessio, Piga, Dario
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Generalized angle vectors, geometric lattices, and flag-angles
, 2021 Interior and exterior angle vectors of polytopes capture curvature information at faces of all dimensions and can be seen as metric variants of $f$-vectors.
Backman, Spencer +2 more
core
On \pi-surfaces of four-dimensional parallelohedra [PDF]
, 2013 We show that every four-dimensional parallelohedron P satisfies a recently found condition of Garber, Gavrilyuk & Magazinov sufficient for the Voronoi conjecture being true for P. Namely we show that for every four-dimensional parallelohedron P the group
Garber, Alexey
core +1 more source
A brief survey on lattice zonotopes [PDF]
Algebraic and Geometric Combinatorics on Lattice Polytopes, 2019 Zonotopes are a rich and fascinating family of polytopes, with connections to many areas of mathematics. In this article we provide a brief survey of classical and recent results related to lattice zonotopes. Our emphasis is on connections to combinatorics, both in the sense of enumeration (e.g. Ehrhart theory) and combinatorial structures (e.g. graphs
Braun, Benjamin +1 more
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Isoperimetric problems for zonotopes
Mathematika, 2023 AbstractShephard (Canad. J. Math. 26 (1974), 302–321) proved a decomposition theorem for zonotopes yielding a simple formula for their volume. In this note, we prove a generalization of this theorem yielding similar formulae for their intrinsic volumes.
Joós, Antal, Lángi, Zsolt
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Generalized Integer Partitions, Tilings of Zonotopes and Lattices
, 2000 In this paper, we study two kinds of combinatorial objects, generalized integer partitions and tilings of two dimensional zonotopes, using dynamical systems and order theory.
BA Davey +12 more
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