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» Realization of Posets
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ARSCOM
2006
81views more  ARSCOM 2006»
14 years 10 months ago
A Counting of the minimal realizations of the posets of dimension two
The posets of dimension 2 are those posets whose minimal realizations have two elements, that is, which may be obtained as the intersection of two of their linear extensions. Gall...
Pierre Ille, Jean-Xavier Rampon
JGAA
2002
74views more  JGAA 2002»
14 years 10 months ago
Realization of Posets
We prove a very general representation theorem for posets and, as a corollary, deduce that any abstract simplicial complex has a geometric realization in the Euclidean space of di...
Patrice Ossona de Mendez
87
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CORR
2008
Springer
92views Education» more  CORR 2008»
14 years 10 months ago
Bipolarization of posets and natural interpolation
The Choquet integral w.r.t. a capacity can be seen in the finite case as a parsimonious linear interpolator between vertices of [0, 1]n. We take this basic fact as a starting poin...
Michel Grabisch, Christophe Labreuche
CORR
2011
Springer
159views Education» more  CORR 2011»
14 years 5 months ago
Geodesics in CAT(0) Cubical Complexes
We describe an algorithm to compute the geodesics in an arbitrary CAT(0) cubical complex. A key tool is a correspondence between cubical complexes of global non-positive curvature ...
Federico Ardila, Megan Owen, Seth Sullivant
EJC
2006
14 years 10 months ago
The positive Bergman complex of an oriented matroid
We study the positive Bergman complex B+ (M) of an oriented matroid M, which is a certain subcomplex of the Bergman complex B(M) of the underlying unoriented matroid M. The positiv...
Federico Ardila, Caroline J. Klivans, Lauren Willi...