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14 papers · 2 filters
Congruences on the Number of Restricted -ary Partitions
Qing-Hu Hou, Hai-Tao Jin, Yan-Ping Mu +1
Andrews, Brietzke, Rødseth and Sellers proved an infinite family of congruences on the number of the restricted -ary partitions when is a prime. In this note, we show that t…
Some Ratio Monotonic Properties of a New Kind of Numbers introduced by Z.-W. Sun
Brian Y. Sun
Recently, Z. W. Sun introduced a new kind of numbers and also posed a conjecture on ratio monotonicity of combinatorial sequences related to . In this paper, by investig…
On Ratio Monotonicity of a New Kind of Numbers Conjectured by Z.-W. Sun
Brian Y. Sun
Recently, Z. W. Sun put forward a series of conjectures on monotonicity of combinatorial sequences in the form of and $\{\sqrt[n+1]{z_{n+1}}/\sqrt[n]…
Total proper connection of graphs
Hui Jiang, Xueliang Li, Yingying Zhang
A graph is said to be {\it total-colored} if all the edges and the vertices of the graph is colored. A path in a total-colored graph is a {\it total proper path} if any two a…
Hardness result for the total rainbow -connection of graphs
Wenjing Li, Xueliang Li, Di Wu
A path in a total-colored graph is called \emph{total rainbow} if its edges and internal vertices have distinct colors. For an -connected graph and an integer with $1…
The Log-Behavior of and
William Y. C. Chen, Ken Y. Zheng
Let denote the partition function. Desalvo and Pak proved the log-concavity of for and the inequality $\frac{p(n-1)}{p(n)}\left(1+\frac{1}{n}\right)>\frac{p(n)…