Journal of Integer Sequences, Vol. 21 (2018), Article 18.7.4

Combinatorial Identities Associated with a Multidimensional Polynomial Sequence


Isabel Cação and Helmuth R. Malonek
CIDMA and Department of Mathematics
University of Aveiro
3810-193 Aveiro
Portugal

M. Irene Falcão
CMAT and Department of Mathematics and Applications
University of Minho
4710-057 Braga
Portugal

Graça Tomaz
CIDMA and Research Unit for Inland Development
Department of Mathematics
Polytechnic of Guarda
6300-659 Guarda
Portugal

Abstract:

In this paper we combine the knowledge of different structures of a special Appell multidimensional polynomial sequence with the problem of establishing combinatorial identities. The elements of this special polynomial sequence have values in a Clifford algebra, are homogeneous hypercomplex differentiable functions of different degrees and their coefficients properties can be used to stress interesting matrix and combinatorial relations.

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(Concerned with sequences A000165 A000302 A000466 A001790 A004736 A005408 A026741 A037012 A046161 A078817 A098597 A099398 A099399 A120777 A162540 A182533 A230206 A230207 A230208 A230209 A230210 A230211 A230212 A283208.)

Received July 21 2018; revised version received August 6 2018. Published in Journal of Integer Sequences, August 23 2018.

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