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math.CO2005
A combinatorial identity with application to Catalan numbers
Hao Pan, Zhi-Wei Sun
By a very simple argument, we prove that if are nonnegative integers then $$\sum_{k=0}^l(-1)^{m-k}\binom{l}{k}\binom{m-k}{n}\binom{2k}{k-2l+m} =\sum_{k=0}^l\binom{l}{k}\bin…
math.CO2005
Arithmetic properties of q-Fibonacci numbers and q-Pell numbers
Hao Pan
We investigate some arithmetic properties of the q-Fibonacci numbers and the q-Pell numbers.
math.CO2005
A congruence involving products of -binomial coefficients
Hao Pan, Hui-Qin Cao
In this paper we establish a -analogue of a congruence of Sun concerning the products of binomial coefficients modulo the square of a prime.
math.CO2005
Restricted sumsets and a conjecture of Lev
Hao Pan, Zhi-Wei Sun
Let A,B,S be finite subsets of an abelian group G. Suppose that the restricted sumset C={a+b: a in A, b in B, and a-b not in S} is nonempty and some c in C can be written as a+b wi…