20.500.12556/DiRROS-25146 Eigenspace embeddings of imprimitive association schemes For a given symmetric association scheme $\mathcal{A}$ and its eigenspace $S_j$ there exists a mapping of vertices of $\mathcal{A}$ to unit vectors of $S_j$, known as the spherical representation of $\mathcal{A}$ in $S_j$, such that the inner products of these vectors only depend on the relation between the corresponding vertices; furthermore, these inner products only depend on the parameters of $\mathcal{A}$. We consider parameters of imprimitive association schemes listed as open cases in the list of parameters for quotient-polynomial graphs recently published by Herman and Maleki, and study embeddings of their substructures into some eigenspaces consistent with spherical representations of the putative association schemes. Using this, we obtain nonexistence for two parameter sets for $4$-class association schemes and one parameter sets for a $5$-class association scheme passing all previously known feasibility conditions, as well as uniqueness for two parameter sets for $5$-class association schemes. association scheme imprimitivity spherical representation nonexistence uniqueness asociativne sheme imprimitivnost sferična reprezentacija neobstoj enoličnost true false true Angleški jezik Slovenski jezik Neznano 2026-01-12 14:47:59 2026-01-12 14:48:00 2026-01-13 03:45:18 0000-00-00 00:00:00 2026 0 0 35 str. iss. 1, article no. P1.2 Vol. 33 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2026-01-01 519.17 1077-8926 10.37236/14071 264381187 14071-PDF_file-58445-4-10-20260112.pdf 14071-PDF_file-58445-4-10-20260112.pdf 1 9C1B337ACD8444C495B3807B8C1F0DDF 097e617fc74137fd8ba7fcbcf9546f77a965d41d86fe36ef494c7cfec42b6e86 b35faaba-efbd-11f0-94a7-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=37887 https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33i1p2 1 53231bf7-efbd-11f0-94a7-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=37884 Inštitut za matematiko, fiziko in mehaniko 0 0 0