# simplicial complex

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## simplicial complex

[sim′plish·əl ′käm‚pleks]
(mathematics)
A set consisting of finitely many simplices where either two simplices are disjoint or intersect in a simplex which is a face common to each. Also known as geometric complex.
References in periodicals archive ?
Let [DELTA](B[X, Y)) be the order complex of the poset B[X, Y]\{y}: it is the simplicial complex whose vertex set is B[X, Y]\{y} and whose simplices are the finite chains in the poset.
Viewed as a CW-complex, M then has the same homotopy type of a simplicial complex which affords further considerations particularly when reducing matters to a skeletal-like, graph-theoretic analysis.
Define a simplicial complex [DELTA]([PHI]) as the set of all subsets A [subset or equal to] [[PHI].
A (geometric) simplicial complex [DELTA] is a finite family of simplices such that (i) if F is in [DELTA] and G is a face of F, then G is also in [DELTA], and (ii) for any two elements F and H of [DELTA], F [intersection] H is a face of both F and H.
More generally, the face lattice of its polar is isomorphic to the simplicial complex of crossing-free subsets of internal diagonals of the (d + 3)-gon.
Recall here that a flag simplicial complex is the complex of cliques of a graph.
The primary difference between a simplicial poset and a simplicial complex is that any pair of faces in a simplicial complex intersect along a single (possibly empty) face of their boundaries; whereas a pair of faces in a simplicial poset can intersect along any sub complex of their boundaries.
If E is a graph, then M([SIGMA]) is its usual graphic matroid, while if E is a simplicial complex then M (E) is its simplicial matroid (see Cordovil and Lindstrom [1987]).
The collection of c-clusters forms a simplicial complex on the set [[PHI].
In Section 6 the cd-index of the nth semisuspension of a non-pure shellable simplicial complex is determined.
For a simplicial complex [DELTA] and its face F [member of] [DELTA], the link of F in [DELTA] is the simplicial complex
Miller [KM04] define the subword complex SC (Q, [rho]) to be the simplicial complex of those subwords of Q whose complements contain a reduced expression for [rho] as a subword.

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