## Michael J. Schlosser and Meesue Yoo

# Weight-dependent commutation relations and combinatorial identities

### (20 pages)

**Abstract.**
We derive combinatorial identities for variables satisfying
specific systems of commutation relations, in particular elliptic
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 derive results for an elliptic derivative of quasicommuting variables,
and finally study weight-dependent extensions of the Weyl algebra
which we connect to rook theory.

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