### Abstract

Combinatorial invariants of a finite simplicial complex K are considered that are functions of the number α_{i}(K) of Simplexes of dimension i of this complex. The main result is Theorem 2, which gives the necessary and sufficient condition for two complexes K and L to have subdivisions K' and L' such that α_{i}(K')=α_{i}(L') for 0 ≤ ∞. The theorem yields a corollary: if the polyhedra |K| and |L| are homeomorphic, then there exist subdivisions K' and L' such that α_{i}(K')=α_{i}(L') for i≥0.

Original language | English (US) |
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Pages (from-to) | 326-332 |

Number of pages | 7 |

Journal | Mathematical Notes of the Academy of Sciences of the USSR |

Volume | 3 |

Issue number | 5 |

DOIs | |

State | Published - May 1968 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Gromov, M. L. (1968). On the number of simplexes of subdivisions of finite complexes.

*Mathematical Notes of the Academy of Sciences of the USSR*,*3*(5), 326-332. https://doi.org/10.1007/BF01150983