Spherical Embeddings of Symmetric Association Schemes in 3-Dimensional Euclidean Space

Abstract

We classify the symmetric association schemes with faithful spherical embedding in 3-dimensional Euclidean space. Our result is based on previous research on primitive association schemes with m 1 = 3.

Classification of partially metric Q-polynomial association schemes with $m_1 = 4$

“…Though Bannai-Ito conjecture and its dual, proved by Bang-Dubickas-Koolen-Moulton [1] and Martin-Williford [17], guarantees the finiteness of P-polynomial (Q-polynomial) association schemes of given valency (multiplicity), the classification of Q-polynomial association schemes of small multiplicity is still yet undone. Bannai and the author revisit the paper [2] and obtain the classification of Q-polynomial association schemes with m 1 = 3 in [5]. We aim to finish the classification of Q-polynomial association schemes with m 1 = 4.…”