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|Title:||Combinatorial identities in the context of hypercomplex function theory|
Falcão, M. I.
Malonek, H. R.
|Publisher:||American Institute of Physics|
|Journal:||AIP Conference Proceedings|
|Abstract(s):||Recently, the authors have shown that a certain combinatorial identity in terms of generators of quaternions is related to a particular sequence of rational numbers (Vietoris' number sequence). This sequence appeared for the first time in a theorem by Vietoris (1958) and plays an important role in harmonic analysis and in the theory of stable holomorphic functions in the unit disc. We present a generalization of that combinatorial identity involving an arbitrary number of generators of a Clifford algebra. The result reveals new insights in combinatorial phenomena in the context of hypercomplex function theory.|
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