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An octonion algebra originating in combinatorics

Authors: Dragomir Ž. Đoković and Kaiming Zhao
Journal: Proc. Amer. Math. Soc. 138 (2010), 4187-4195
MSC (2010): Primary 17A75, 05B20, 05B30
Published electronically: June 22, 2010
MathSciNet review: 2680045
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Abstract: C.H. Yang discovered a polynomial version of the classical Lagrange identity expressing the product of two sums of four squares as another sum of four squares. He used it to give short proofs of some important theorems on composition of $ \delta$-codes (now known as $ T$-sequences). We investigate the possible new versions of his polynomial Lagrange identity. Our main result shows that all such identities are equivalent to each other.

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Additional Information

Dragomir Ž. Đoković
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

Kaiming Zhao
Affiliation: Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5, Canada –and– Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China

Keywords: Laurent polynomial ring, polynomial Lagrange identity, octonion algebra, composition algebra
Received by editor(s): May 12, 2009
Received by editor(s) in revised form: September 21, 2009, and February 13, 2010
Published electronically: June 22, 2010
Additional Notes: The first author was supported by an NSERC Discovery Grant.
The second author was supported by the NSERC and the NSF of China (Grant 10871192).
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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