On the isomorphism of certain primitive Q-polynomial not\n P-polynomial association schemes

2020/09/07 by Giusy Monzillo, Monzillo, Giusy, Alessandro Siciliano +1
Computer Science · Mathematics · #05E30 #51E20 #Advanced Algebra and Geometry #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2009.03159

openalex publication_date 2020/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 2011, Penttila and Williford constructed an infinite new family of\nprimitive Q-polynomial 3-class association schemes, not arising from distance\nregular graphs, by exploring the geometry of the lines of the unitary polar\nspace H(3,q²), q even, with respect to a symplectic polar space W(3,q)\nembedded in it.\n In a private communication to Penttila and Williford, H.~Tanaka pointed out\nthat these schemes have the same parameters as the 3-class schemes found by\nHollmann and Xiang in 2006 by considering the action of \PGL(2,q²),\nq even, on a non-degenerate conic of \PG(2,q²) extended in\n\PG(2,q⁴). Therefore, the question arises whether the above\nassociation schemes are isomorphic. In this paper we provide the positive\nanswer. As by product, we get an isomorphism of strongly regular graphs.\n

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