Lilu Zhao

most citedSome congruences for the second-order Catalan numbers

6 citations · 6 across the 2 of their papers we have counts for

collaborators

2 papers

math.NT2009★ 6 cited

Some congruences for the second-order Catalan numbers

Li-Lu Zhao, Hao Pan, Zhi-Wei Sun

Let p be any odd prime. We mainly show that $k = 1 \sum p - 1 bin o mia l (3 k, k) * 2^{k} / k = 0 (m o d p)$ and $k = 1 \sum p - 1 2^{k - 1} C_{k}^{(2)} = (- 1)^{(p - 1) /2} - 1 (m o d p),$ where $C_k^{(2)}=b…

math.CO2008

Clique Numbers of Graphs and Irreducible Exact m-Covers of Z

Hao Pan, Li-Lu Zhao

For each m>=1 and k>=2, we construct a graph G=(V,E) with ω(G)=m such that max_{1\leq i\leq k} ω(G[V_i])=m for arbitrary partition V=V_1\cup...\cup V_k, where ω(G) is the clique nu…