Displaying similar documents to “A combinatorial interpretation for an identity of Barrucand.”

The Catalan Numbers. Part II 1

Karol Pąk (2006)

Formalized Mathematics

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In this paper, we define sequence dominated by 0, in which every initial fragment contains more zeroes than ones. If n ≥ 2 · m and n > 0, then the number of sequences dominated by 0 the length n including m of ones, is given by the formula [...] and satisfies the recurrence relation [...] Obviously, if n = 2 · m, then we obtain the recurrence relation for the Catalan numbers (starting from 0) [...] Using the above recurrence relation we can see that [...] where [...] and hence [...]...

Ramsey's Theorem

Marco Riccardi (2008)

Formalized Mathematics

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The goal of this article is to formalize two versions of Ramsey's theorem. The theorems are not phrased in the usually pictorial representation of a coloured graph but use a set-theoretic terminology. After some useful lemma, the second section presents a generalization of Ramsey's theorem on infinite set closely following the book [9]. The last section includes the formalization of the theorem in a more known version (see [1]).MML identifier: RAMSEY 1, version: 7.9.01 4.101.1015 ...