This document provides a summary of the basic principles and formulas used in permutations and combinations, which are fundamental concepts in combinatorics. These tools are essential in various ...

$$ \begin{array}{l}{C\left(n, n_{1}\right) C\left(n-n_{1}, n_{2}\right) \cdots C\left(n-n_{1}-\cdots-n_{k-1}, n_{k}\right)} \ {=\frac{n !}{n_{1} !\left(n-n_{1}\right ...

DIMAP and Mathematic Institute, University of Warwick, Coventry CV4 7AL, UK Research of this author was supported by the Centre for Discrete Mathematics and Its Applications (DIMAP), University of ...

Abstract: STEM educators have devoted increasing attention to discrete mathematics in recent years due, in part, to its strong connections with subjects like computer science, probability and ...

Preparation for any exam requires an overall understanding and a rigorous practice of all the concepts to be tested in that exam. This can be achieved by a thorough learning of each topic given in the ...

ABSTRACT: The spectral properties of special matrices have been widely studied, because of their applications. We focus on permutation matrices over a finite field and, more concretely, we compute the ...

Engineering section of JagranJosh brings Online Test for JEE MAIN, JEE Advanced, UPSEEE, WBJEE and other engineering entrance examination to help the students in improving their performance and ...

Abstract: To achieve the Shannon's confusion and diffusion properties, an image encryption algorithm should include permutations and substitutions. This paper presents three different permutation ...