Geodesic
On~the number of triangulation simplexes
Izvestiya. Mathematics , Tome 44 (1995) no. 1, pp. 1-20.

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We consider generating functions for the number of triangulation simplexes. We show that the binomial generating function is multiplicative. Certain exponential generating functions turn out to be solutions of evolutionary differential equations. We get congruences for the number of internal simplexes of certain triangulations generalizing the Staudt congruences for Bernoulli numbers. 
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M. Kh. Gizatullin. On~the number of triangulation simplexes. Izvestiya. Mathematics , Tome 44 (1995) no. 1, pp. 1-20. http://geodesic.mathdoc.fr/item/IM2_1995_44_1_a0/

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