Combinatorial problems related to origin–destination matrices

Combinatorial problems related to origin-destination matrices

Bitwise Operations Related to a Combinatorial Problem on Binary Matrices

Some techniques for the use of bitwise operations are described in the article. As an example, an open problem of isomorphism-free generations of combinatorial objects is discussed. An equivalence relation on the set of square binary matrices having the same number of units in each row and each column is defined. Each binary matrix is represented using ordered n-tuples of natural numbers. It is...

Fibonacci sequence related to a combinatorial problem on binary matrices

We discuss an equivalence relation on the set of square binary matrices with the same number of 1’s in each row and each column. Each binary matrix is represented using ordered n-tuples of natural numbers. We give a few starting values of integer sequences related to the discussed problem. The obtained sequences are new and they are not described in the On-Line Encyclopedia of Integer Sequences...

Combinatorial Problems Related to Geometrically Distributed Random Variables

Motivated from Computer Science problems we consider the following situation (compare [2] and [3]). In these papers the reader will find a more complete description as well as additional references. Let X denote a geometrically distributed random variable, i.e. P{X = k} = pqk−1 for k ∈ N and q = 1 − p. Assume that we have n independent random variables X1, . . . , Xn according to this distribut...

the second immanant of some combinatorial matrices

let $a = (a_{i,j})_{1 leq i,j leq n}$ be an $n times n$ matrixwhere $n geq 2$. let $dt(a)$, its second immanant be the immanant corresponding to the partition $lambda_2 = 2,1^{n-2}$. let $g$ be a connected graph with blocks $b_1, b_2, ldots b_p$ and with$q$-exponential distance matrix $ed_g$. we given an explicitformula for $dt(ed_g)$ which shows that $dt(ed_g)$ is independent of the manner in ...