Schlosser, Michael and Yoo, Meesue - Some combinatorial identities involving noncommuting variables

dmtcs:2467 - Discrete Mathematics & Theoretical Computer Science, January 1, 2015, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Some combinatorial identities involving noncommuting variables

Authors: Schlosser, Michael and Yoo, Meesue

We derive combinatorial identities for variables satisfying specific sets of commutation relations. The identities thus obtained extend corresponding ones for $q$-commuting variables $x$ and $y$ satisfying $yx=qxy$. In particular, we obtain weight-dependent binomial theorems, functional equations for generalized exponential functions, we propose a derivative of noncommuting variables, and finally utilize one of the considered weight functions to extend rook theory. This leads us to an extension of the $q$-Stirling numbers of the second kind, and of the $q$-Lah numbers.


Source : oai:HAL:hal-01337755v1
Volume: DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Section: Proceedings
Published on: January 1, 2015
Submitted on: November 21, 2016
Keywords: noncommuting variables,weight dependent binomial theorem,combinatorial identities,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


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