On the number of simplexes of subdivisions of finite complexes

Combinatorial invariants of a finite simplicial complex K are considered that are functions of the number _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 _i(K')=_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 _i(K')=_i(L') for i0.Translated from Matematicheskie Zametki, Vol. 3, No. 5, pp. 511–522, May, 1968.