TY - JOUR

T1 - Deciding shellability of simplicial complexes with h-assignments

AU - Moriyama, Sonoko

PY - 2011/6

Y1 - 2011/6

N2 - If a d-dimensional pure simplicial complex C has a shelling, which is a specific total order of all facets of C, C is said to be shellable. We consider the problem of deciding whether C is shellable or not. This problem is solved in linear time of m, the number of all facets of C, if d = 1 or C is a pseudomanifold in d = 2. Otherwise it is unknown at this point whether the decision of shellability can be solved in polynomial time of m. Thus, for the latter case, we had no choice but to apply a brute force method to the decision problem; namely checking up to the m! ways to see if one can arrange all the m facets of C into a shelling. In this paper, we introduce a new concept, called h-assignment, to C and propose a practical method using h-assignments to decide whether C is shellable or not. Our method can make the decision of shellability of C by smaller sized computation than the brute force method.

AB - If a d-dimensional pure simplicial complex C has a shelling, which is a specific total order of all facets of C, C is said to be shellable. We consider the problem of deciding whether C is shellable or not. This problem is solved in linear time of m, the number of all facets of C, if d = 1 or C is a pseudomanifold in d = 2. Otherwise it is unknown at this point whether the decision of shellability can be solved in polynomial time of m. Thus, for the latter case, we had no choice but to apply a brute force method to the decision problem; namely checking up to the m! ways to see if one can arrange all the m facets of C into a shelling. In this paper, we introduce a new concept, called h-assignment, to C and propose a practical method using h-assignments to decide whether C is shellable or not. Our method can make the decision of shellability of C by smaller sized computation than the brute force method.

KW - H-vectors

KW - Shellability

KW - Simplicial complexes

UR - http://www.scopus.com/inward/record.url?scp=79958013763&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79958013763&partnerID=8YFLogxK

U2 - 10.1587/transfun.E94.A.1238

DO - 10.1587/transfun.E94.A.1238

M3 - Article

AN - SCOPUS:79958013763

VL - E94-A

SP - 1238

EP - 1241

JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

SN - 0916-8508

IS - 6

ER -