On Various Combinatorial Sums and Related Identities
نویسندگان
چکیده
In this talk we give a survey of results and methods on some combinatorial sums involving binomial coefficients and related to Bernoulli and Euler polynomials. We will also talk about certain sums of minima and maxima related to Dedekind sums. Some interesting identities associated with the various sums will also be introduced. 1. A curious identity and the sum ∑ k≡r (mod m) ( n k ) In 1988 Zhi-Wei Sun proved a conjecture of his twin brother Zhi-Hong Sun, later he made a further extension by establishing the following result. Theorem 1.1 [Z. W. Sun, Integers 2(2002)]. Let m ∈ N = {0, 1, 2, . . . }. Then we have the curious identity
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