On Divisibility concerning Binomial Coefficients
نویسندگان
چکیده
Binomial coefficients arise naturally in combinatorics. Recently the speaker initiated the study of certain divisibility properties of binomial coefficients, and products or sums of binomial coefficients. In this talk we introduce the speaker’s related results and various conjectures. The materials come from the author’s two preprints: 1. Z. W. Sun, Products and sums divisible by central binomial coefficients, arXiv:1004.4623. 2. Z. W. Sun, On divisibility concerning binomial coefficients, arXiv:1005.1054. Catalan numbers For n ∈ N = {0, 1, 2, . . .}, the nth Catalan number is given by Cn = 1 n + 1 ( 2n n ) = ( 2n n ) − ( 2n n + 1 ) .
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