On the multiplicities of the primitive idempotents of a Q-polynomial distance-regular graph
Ito, Tanabe and Terwilliger recently introduced the notion of a tridiagonal pair. We apply their results to distance-regular graphs and obtain the following theorem. THEOREM. Let Γ denote a distance-regular graph with diameter D ≥ 3. Suppose Γ is Q-polynomial with respect to the ordering E0, E1,...,...
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2002
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oai:animorepository.dlsu.edu.ph:faculty_research-46082021-09-17T08:20:57Z On the multiplicities of the primitive idempotents of a Q-polynomial distance-regular graph Pascasio, Arlene A. Ito, Tanabe and Terwilliger recently introduced the notion of a tridiagonal pair. We apply their results to distance-regular graphs and obtain the following theorem. THEOREM. Let Γ denote a distance-regular graph with diameter D ≥ 3. Suppose Γ is Q-polynomial with respect to the ordering E0, E1,..., ED of the primitive idempotents. For 0 ≤ i ≤ D, let mi, denote the multiplicity of E i. Then (i) mi-1 ≤ mi (1 ≤ i ≤ D/2), (ii) mi ≤ mD-i (0 ≤ i ≤ D/2). By proving the above theorem we resolve a conjecture of Dennis Stanton. © 2002 Elsevier Science Ltd. All rights reserved. 2002-01-01T08:00:00Z text text/html https://animorepository.dlsu.edu.ph/faculty_research/3606 info:doi/10.1006/eujc.2002.0607 https://animorepository.dlsu.edu.ph/context/faculty_research/article/4608/type/native/viewcontent/eujc.2002.0607 Faculty Research Work Animo Repository Algebras, Linear Polynomials Algebra |
| institution |
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De La Salle University Library |
| continent |
Asia |
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Philippines Philippines |
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De La Salle University Library |
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DLSU Institutional Repository |
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Algebras, Linear Polynomials Algebra |
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Algebras, Linear Polynomials Algebra Pascasio, Arlene A. On the multiplicities of the primitive idempotents of a Q-polynomial distance-regular graph |
| description |
Ito, Tanabe and Terwilliger recently introduced the notion of a tridiagonal pair. We apply their results to distance-regular graphs and obtain the following theorem. THEOREM. Let Γ denote a distance-regular graph with diameter D ≥ 3. Suppose Γ is Q-polynomial with respect to the ordering E0, E1,..., ED of the primitive idempotents. For 0 ≤ i ≤ D, let mi, denote the multiplicity of E i. Then (i) mi-1 ≤ mi (1 ≤ i ≤ D/2), (ii) mi ≤ mD-i (0 ≤ i ≤ D/2). By proving the above theorem we resolve a conjecture of Dennis Stanton. © 2002 Elsevier Science Ltd. All rights reserved. |
| format |
text |
| author |
Pascasio, Arlene A. |
| author_facet |
Pascasio, Arlene A. |
| author_sort |
Pascasio, Arlene A. |
| title |
On the multiplicities of the primitive idempotents of a Q-polynomial distance-regular graph |
| title_short |
On the multiplicities of the primitive idempotents of a Q-polynomial distance-regular graph |
| title_full |
On the multiplicities of the primitive idempotents of a Q-polynomial distance-regular graph |
| title_fullStr |
On the multiplicities of the primitive idempotents of a Q-polynomial distance-regular graph |
| title_full_unstemmed |
On the multiplicities of the primitive idempotents of a Q-polynomial distance-regular graph |
| title_sort |
on the multiplicities of the primitive idempotents of a q-polynomial distance-regular graph |
| publisher |
Animo Repository |
| publishDate |
2002 |
| url |
https://animorepository.dlsu.edu.ph/faculty_research/3606 https://animorepository.dlsu.edu.ph/context/faculty_research/article/4608/type/native/viewcontent/eujc.2002.0607 |
| _version_ |
1767195939624189952 |