# Nonexistence of exceptional imprimitive Q-polynomial association schemes with six classes

@article{Tanaka2011NonexistenceOE, title={Nonexistence of exceptional imprimitive Q-polynomial association schemes with six classes}, author={Hajime Tanaka and Rie Tanaka}, journal={Eur. J. Comb.}, year={2011}, volume={32}, pages={155-161} }

## 9 Citations

On few-class Q-polynomial association schemes: feasible parameters and nonexistence results

- MathematicsArs Mathematica Contemporanea
- 2021

We present the tables of feasible parameters of primitive $3$-class $Q$-polynomial association schemes and $4$- and $5$-class $Q$-bipartite association schemes (on up to $2800$, $10000$, and $50000$…

Twice Q-polynomial distance-regular graphs of diameter 4

- Mathematics
- 2015

It is known that a distance-regular graph with valency k at least three admits at most two Q-polynomial structures. We show that all distance-regular graphs with diameter four and valency at least…

On Q-Polynomial Association Schemes of Small Class

- MathematicsElectron. J. Comb.
- 2012

An inequality involving the third largest or second smallest dual eigenvalues of $Q$-polynomial association schemes of class at least three is shown and can be applied to distance-regular graphs as well.

Uniformity in association schemes and coherent configurations: Cometric Q-antipodal schemes and linked systems

- MathematicsJ. Comb. Theory, Ser. A
- 2013

Cometric Association Schemes.

- Mathematics
- 2019

One may think of a $d$-class association scheme as a $(d+1)$-dimensional matrix algebra over $\mathbb{R}$ closed under Schur products. In this context, an imprimitive scheme is one which admits a…

$Q$-polynomial distance-regular graphs and a double affine Hecke algebra of rank one

- Mathematics
- 2013

Distance-regular graphs

- Mathematics
- 2014

An introduction to distance-regular graphs is presented for the reader who is unfamiliar with the subject, and an overview of some developments in the area of distance- regular graphs since the monograph 'BCN' was written.

On the Connectivity of Graphs in Association Schemes

- Mathematics, Computer ScienceElectron. J. Comb.
- 2017

It is proved that the deletion of the neighborhood of any vertex leaves behind at most one non-singleton component, and the only connected relations in symmetric association schemes which admit a disconnecting set of size two are those which are ordinary polygons.

Implications of vanishing Krein parameters on Delsarte designs, with applications in finite geometry

- Mathematics
- 2021

In this paper we show that if θ is a T -design of an association scheme (Ω , R ), and the Krein parameters q hi,j vanish for some h 6∈ T and all i, j 6∈ T ( i, j, h 6 = 0), then θ consists of…

## References

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There are finitely many Q-polynomial association schemes with given first multiplicity at least three

- MathematicsEur. J. Comb.
- 2009

Uniformity in association schemes and coherent configurations: Cometric Q-antipodal schemes and linked systems

- MathematicsJ. Comb. Theory, Ser. A
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There are only finitely many distance-regular graphs of fixed valency greater than two

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A survey on spherical designs and algebraic combinatorics on spheres

- MathematicsEur. J. Comb.
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Imprimitive Q-polynomial Association Schemes

- Mathematics
- 1998

AbstractIt is well known that imprimitive P-polynomial association schemes
$$\mathcal{X} = (X,\{ R_i \} _{0 \leqslant i \leqslant d} ) $$
with
$$$$
are either bipartite or antipodal, i.e.,…