Section: New Results

Bourbaki in Coq

Participant : José Grimm.

In previous years, we developed a formal library describing the part of the Bourbaki books on set theory, cardinals, and ordinals. The whole development now runs under Coq 8.4, ssreflect 1.4. The main contribution this year is the study of some families of numbers (Stirling numbers of the second kind, Euler numbers, Bell numbers), and their relations to cardinalities (number of partitions of a set, number of partition with $p$ parts, number of surjections $I_n\to I_p$). We have some explicit formulas for ${\sum }_{i<n}{i}^k$ as sums of binomial coefficients.