Realization of Posets
Copyright policy )Realization of Posets
We prove a very general representation theorem for posets and, as a corollary, deduce that any abstract simplicial complex S has a geometric realization in the Euclidean space of dimension P(S)-1, where P(S) is the Dushnik-Miller dimension of the face order of S.
Dushnik-Miller dimension, geometric realization, Algebraic aspects of posets, representation theorem, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], posets, geometric convexity, Abstract complexes in algebraic topology, abstract simplicial complex, Euclidean space, Algebraic combinatorics, poset dimension, order dimension, face order
Dushnik-Miller dimension, geometric realization, Algebraic aspects of posets, representation theorem, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], posets, geometric convexity, Abstract complexes in algebraic topology, abstract simplicial complex, Euclidean space, Algebraic combinatorics, poset dimension, order dimension, face order
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