2011/06/10 by Michael J. Schlosser, Schlosser, Michael J.
Computer Science · Mathematics · #11B65 #33E05 #33E20 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Polynomial and algebraic computation #Primary 16T30 #Quantum Algebra (math.QA) #Secondary 05A30 #math.CO #math.QA #msc:05A30 #msc:11B65 #msc:16T30 #msc:33E05 #msc:33E20
paper · pdf · doi:10.48550/arxiv.1106.2112
23 pages; flaws in the definition of the algebra corrected
openalex publication_date 2011/06/10 · arxiv created 2012/03/16 · arxiv updated 2012/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A weight-dependent generalization of the binomial theorem for noncommuting variables is presented. This result extends the well-known binomial theorem for q-commuting variables by a generic weight function depending on two integers. For a special case of the weight function, restricting it to depend on only a single integer, the noncommutative binomial theorem involves an expansion of complete symmetric functions. Another special case concerns the weight function to be a suitably chosen elliptic (i.e., doubly-periodic meromorphic) function, in which case an elliptic generalization of the binomial theorem is obtained. The latter is utilized to quickly recover Frenkel and Turaev's elliptic hypergeometric 10V9 summation formula, an identity fundamental to the theory of elliptic hypergeometric series.