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# Is there a way to check if a given simplicial complex is a pseudomanifold with boundary?

Def: A pseudomanifold with boundary is a simplicial complex with the following properties: โข it is pure of some dimension ๐ (all of its facets are ๐-dimensional) โข every (๐ โ 1)-dimensional simplex is the face of at most two facets โข for every two facets ๐ and ๐ , there is a sequence of facets ๐ = ๐_0, ๐_1, ..., ๐_๐ = ๐ such that for each ๐, ๐_๐ and ๐_{๐โ1} intersect in a (๐ โ 1)-simplex

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It should be easy to modify the is_pseudomanifoldmethod at https://github.com/sagemath/sage/blob.... Untested:

def is_pseudomanifold_with_boundary(K):
if not K.is_pure():
return False
d = K.dimension()
if d == 0:
return len(K.facets()) == 2
F = K.facets()
X = K.faces()[d-1]
# is each (d-1)-simplex is the face of at most two facets?
# *** This is the only change when compared to is_pseudomanifold. ***
for s in X:
if len([a for a in [s.is_face(f) for f in F] if a]) > 2:
return False
# construct a graph with one vertex for each facet, one edge
# when two facets intersect in a (d-1)-simplex, and see
# whether that graph is connected.
return K.flip_graph().is_connected()

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Asked: 2023-06-21 13:06:22 +0200

Seen: 88 times

Last updated: Jun 22 '23