| Title: | Eigenspace embeddings of imprimitive association schemes |
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| Authors: | ID Vidali, Janoš (Author) |
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| Files: |  PDF - Presentation file, download (599,37 KB)
MD5: 9C1B337ACD8444C495B3807B8C1F0DDF
 URL - Source URL, visit https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33i1p2
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | 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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| Keywords: | association scheme, imprimitivity, spherical representation, nonexistence, uniqueness |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.01.2026 |
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| Year of publishing: | 2026 |
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| Number of pages: | 35 str. |
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| Numbering: | Vol. 33, iss. 1, article no. P1.2 |
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| PID: | 20.500.12556/DiRROS-25146  |
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| UDC: | 519.17 |
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| ISSN on article: | 1077-8926 |
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| DOI: | 10.37236/14071 |
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| COBISS.SI-ID: | 264381187 |
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| Note: |
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| Publication date in DiRROS: | 12.01.2026 |
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| Views: | 236 |
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| Downloads: | 167 |
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