| Naslov: | Eigenspace embeddings of imprimitive association schemes |
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| Avtorji: | ID Vidali, Janoš (Avtor) |
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| Datoteke: |  PDF - Predstavitvena datoteka, prenos (599,37 KB)
MD5: 9C1B337ACD8444C495B3807B8C1F0DDF
 URL - Izvorni URL, za dostop obiščite https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33i1p2
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| Jezik: | Angleški jezik |
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| Tipologija: | 1.01 - Izvirni znanstveni članek |
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| Organizacija: |  IMFM - Inštitut za matematiko, fiziko in mehaniko
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| Povzetek: | 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. |
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| Ključne besede: | association scheme, imprimitivity, spherical representation, nonexistence, uniqueness |
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| Status publikacije: | Objavljeno |
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| Verzija publikacije: | Objavljena publikacija |
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| Datum objave: | 01.01.2026 |
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| Leto izida: | 2026 |
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| Št. strani: | 35 str. |
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| Številčenje: | Vol. 33, iss. 1, article no. P1.2 |
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| PID: | 20.500.12556/DiRROS-25146  |
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| UDK: | 519.17 |
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| ISSN pri članku: | 1077-8926 |
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| DOI: | 10.37236/14071 |
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| COBISS.SI-ID: | 264381187 |
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| Opomba: |
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| Datum objave v DiRROS: | 12.01.2026 |
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| Število ogledov: | 239 |
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| Število prenosov: | 168 |
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| Metapodatki: |    |
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