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References (6)
-
E. Bannai, Tatsuro Ito (1984)
Algebraic Combinatorics I: Association Schemes -
A. Hora, N. Obata (2007)
Distance-Regular Graphs -
Paul Terwilliger, Chalermpong Worawannotai (2012)
Augmented down-up algebras and uniform posetsArs Math. Contemp., 6
-
Štefko Miklavič, Paul Terwilliger (2011)
Bipartite Q-polynomial distance-regular graphs and uniform posetsJournal of Algebraic Combinatorics, 38
-
Paul Terwilliger (1990)
The Incidence Algebra of a Uniform Poset -
(1992)
The subconstituent algebra of an association scheme I
- Publisher
- Springer Journals
- Copyright
- Copyright © 2018 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature
- Subject
- Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
- ISSN
- 0168-9673
- eISSN
- 1618-3932
- DOI
- 10.1007/s10255-018-0745-y
- Publisher site
- See Article on Publisher Site
Abstract
Let Γ denote the folded (2D + 1)-cube with vertex set X and diameter D ≥ 3. Fix x ∈ X. We first define a partial order ≤ on X as follows. For y, z ∈ X let y ≤ z whenever ∂(x, y) + ∂(y, z) = ∂(x, z). Let R (resp. L) denote the raising matrix (resp. lowering matrix) of Γ. Next we show that there exists a certain linear dependency among RL 2, LRL,L 2 R and L for each given Q-polynomial structure of Γ. Finally, we determine whether the above linear dependency structure gives this poset a uniform structure or strongly uniform structure.
Journal
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Apr 26, 2018