For this, a sufficient combinatorial property is that all of the antichains of this poset are countable.
2.
Indeed, every combinatorial property of one Platonic solid can be interpreted as another combinatorial property of the dual.
3.
Indeed, every combinatorial property of one Platonic solid can be interpreted as another combinatorial property of the dual.
4.
The theory of abstract polytopes attempts to detach polytopes from the space containing them, considering their purely combinatorial properties.
5.
Rota later applied umbral calculus extensively in his paper with Shen to study the various combinatorial properties of the cumulants.
6.
These algebras form a generalization of finite-dimensional semisimple Lie algebras, and share many of their combinatorial properties.
7.
There is no natural complex analogue of the ordering of points on a real line ( or of the associated combinatorial properties ).
8.
Due to projective duality, many statements about the combinatorial properties of points in the plane may be more easily understood in an equivalent dual form about arrangements of lines.
9.
The theory of topological graphs is an area of graph theory, mainly concerned with combinatorial properties of topological graphs, in particular, with the crossing patterns of their edges.
10.
The conceptual issues raised by complex polytopes, non-convexity, duality and other phenomena led Gr�nbaum and others to the more general study of abstract combinatorial properties relating vertices, edges, faces and so on.
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