## Abstract

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.

Original language | English |
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Pages (from-to) | 1238-1241 |

Number of pages | 4 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E94-A |

Issue number | 6 |

DOIs | |

Publication status | Published - 2011 Jun |

## Keywords

- H-vectors
- Shellability
- Simplicial complexes

## ASJC Scopus subject areas

- Signal Processing
- Computer Graphics and Computer-Aided Design
- Electrical and Electronic Engineering
- Applied Mathematics