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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
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…
math.CO2004
On various restricted sumsets
Zhi-Wei Sun, Yeong-Nan Yeh
For finite subsets A_1,...,A_n of a field, their sumset is given by {a_1+...+a_n: a_1 in A_1,...,a_n in A_n}. In this paper we study various restricted sumsets of A_1,...,A_n with…