Eigenspace embeddings of imprimitive association schemes

Vidali, Janoš (avtor)

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.

• Jezik: Angleški jezik
• Ključne besede: association scheme, imprimitivity, spherical representation, nonexistence, uniqueness
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Datum objave: 01.01.2026
• Leto izida: 2026
• Št. strani: 35 str.
• Številčenje: Vol. 33, iss. 1, article no. P1.2
• PID: 20.500.12556/RUL-177899
• UDK: 519.17
• ISSN pri članku: 1077-8926
• DOI: 10.37236/14071
• COBISS.SI-ID: 264381187
• Datum objave v RUL: 12.01.2026

Gradivo je del revije

• Naslov: The Electronic journal of combinatorics
• Skrajšan naslov: Electron. j. comb.
• Založnik: N.J. Calkin and H.S. Wilf
• ISSN: 1077-8926
• COBISS.SI-ID: 6973785

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: asociativne sheme, imprimitivnost, sferična reprezentacija, neobstoj, enoličnost