11 citations · 29 across the 23 of their papers we have counts for
5 papers · 1 filter
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…
A number-theoretic approach to homotopy exponents of SU(n)
Donald M. Davis, Zhi-Wei Sun
We use methods of combinatorial number theory to prove that, for each and any prime , some homotopy group contains an element of order …
A sharp result on m-covers
Hao Pan, Zhi-Wei Sun
Let A={a_s+n_sZ}_{s=1}^k be a finite system of arithmetic sequences which forms an m-cover of Z (i.e., every integer belongs at least to m members of A). In this paper we show the…
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…
Finite covers of groups by cosets or subgroups
Zhi-Wei Sun
This paper deals with combinatorial aspects of finite covers of groups by cosets or subgroups. Let be left cosets in a group such that co…