@ARTICLE{10.21494/ISTE.OP.2021.0695, TITLE={Permutation (Matrices) and Beyond}, AUTHOR={Richard A. Brualdi, }, JOURNAL={Advances in Pure and Applied Mathematics}, VOLUME={12}, NUMBER={Issue 3 (Special AUS-ICMS 2020)}, YEAR={2021}, URL={http://www.openscience.fr/Permutation-Matrices-and-Beyond}, DOI={10.21494/ISTE.OP.2021.0695}, ISSN={1869-6090}, ABSTRACT={This is an exposition of my keynote talk given at The Third International Conference on Mathematics and Statistics: AUS-ICMS February 2020, Sharjah, UAE. It concerns permutations and permutation matrices, and some of their generalizations. It is not intended to be comprehensive in the topics discussed, but to highlight some aspects. The final section discusses a number of open problems and conjectures. A number of references are provided to get one started on a more comprehensive study.}}