M. Horn: Pauli Pascal Pyramids, Pauli Fibonacci/Jacobsthal Numbers


Pauli Pascal Pyramids, Pauli Fibonacci Numbers, and Pauli Jacobsthal Numbers

by Martin Erik Horn
E-Mail: horn@fhw-berlin.de, mail@grassmann-algebra.de

Abstract:
The three anti-commutative two-dimensional Pauli Pascal triangles can be
generalized into multi-dimensional Pauli Pascal hyperpyramids.

Fibonacci and Jacobsthal numbers are then generalized into Pauli Fibonacci
numbers, Pauli Jacobsthal numbers, and Pauli Fibonacci numbers of higher order.

And the question is: Are Pauli rabbits killer rabbits?

Contents
1. Introduction
2. Pascal Triangles
3. Pascal Pyramids and Pascal Hyperpyramids
4. Basic Elements of Geometric Algebra
5. Anti-commutative Pauli Pascal Triangles
6. Pauli Pascal Pyramids and Pauli Pascal Hyperpyramids
7. Positive and Negative Fibonacci Numbers
8. Pauli Fibonacci Numbers
9. Jacobsthal Numbers and Pauli Jacobsthal Numbers
10. Fibonacci Numbers and Pauli Fibonacci Numbers of Higher Order
11. Outlook
12. Literature

Received:
29. December 2007

Download: http://arxiv.org/abs/0711.4030

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