An octonion algebra originating in combinatorics
D.Z. Djokovic, K. Zhao

TL;DR
This paper explores new polynomial identities related to octonion algebra originating from combinatorics, showing their equivalence and connecting them to classical sum of squares identities.
Contribution
It demonstrates that all polynomial Lagrange identities derived from combinatorics are fundamentally equivalent, extending the classical sum of squares identities to octonion algebra.
Findings
All new identities are equivalent to each other.
Connections established between combinatorial identities and octonion algebra.
Extension of classical sum of squares identities to polynomial forms.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
Topicsgraph theory and CDMA systems · semigroups and automata theory · Coding theory and cryptography
