Some properties of deformed $q$-numbers

Thierry C. Petit Lobão, Pedro G. S. Cardoso, Suani T. R. Pinho, Ernesto P. Borges

Published 2009-01-28Version 1

Nonextensive statistical mechanics has been a source of investigation in mathematical structures such as deformed algebraic structures. In this work, we present some consequences of $q$-operations on the construction of $q$-numbers for all numerical sets. Based on such a construction, we present a new product that distributes over the $q$-sum. Finally, we present different patterns of $q$-Pascal's triangles, based on $q$-sum, whose elements are $q$-numbers.