Combinatorial invariants of a finite simplicial complex K are considered that are functions of the number αi(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 αi(K')=αi(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 αi(K')=αi(L') for i≥0.
|Original language||English (US)|
|Number of pages||7|
|Journal||Mathematical Notes of the Academy of Sciences of the USSR|
|State||Published - May 1968|
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