A general theorem for providing a class of combinatorial identities where the sum is over all the partitions of a positive integer is proven. Five examples as the applications of ...
Given an undirected hypergraph and a subset of vertices S ⊆ V with a specified root vertex r ∈ S, the STEINER ROOTED-ORIENTATION problem is to find an orientation of all the...
— This paper considers networks consisting of integral input-to-state stable (iISS) subsystems and addresses the problem of verifying iISS property of a given network. First, we ...
We introduce a concept of so-called disjoint ordering for any collection of finite sets. It can be viewed as a generalization of a system of distinctive representatives for the s...
Let Fk(x) = n=0 Fk n xn . Using the interpretation of Fibonacci numbers in the terms of Morse codes, we give a bijective proof of Riordan's formula (1 - Lkx + (-1)k x2 )Fk(x...