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Feasibility conditions for non-symmetric 3-class association schemes
1996
Discrete Mathematics
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In this paper a set of necessary conditions for the existence of a non-symmetric 3-class association scheme expressed in terms of its symmetric closure will be given. ...
In this vein we consider in this paper a symmetric 2-scheme (we shall call an n-class association scheme briefly an n-scheme) and ask under what conditions on the parameters it is feasible that such a ...
of a non-symmetric 3-scheme. ...
doi:10.1016/0012-365x(96)00103-3
fatcat:6nr5kt24vfcjdmw2dbxvcwidcy
Class 3 association schemes whose symmetrizations have two classes
1995
Journal of combinatorial theory. Series A
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For a given commutative association scheme 2", by fusing all the non-self-paired relations pairwise with their symmetric counterparts, we can obtain a new symmetric association scheme Y. ...
In this paper, we investigate when a symmetric association scheme ~" of class 2 admits a symmetrizable commutative fission scheme 2" of class 3. ...
as the symmetrization of a non-symmetric commutative association scheme of class 3. ...
doi:10.1016/0097-3165(95)90077-2
fatcat:k22n22esn5gonowswuq6aqikyq
Algorithmic Approach to Non-symmetric 3-class Association Schemes
[chapter]
2009
Algorithmic Algebraic Combinatorics and Gröbner Bases
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There are 24 feasible parameter sets for a primitive non-symmetric association schemes with 3 classes and at most 100 vertices. ...
We also consider directed graphs that satisfy only some of the conditions required for a non-symmetric association scheme with 3 classes. ...
Ito [19] has proved that a non-symmetric 3-class association scheme with µ = λ does not satisfy the feasibility condition. ...
doi:10.1007/978-3-642-01960-9_8
fatcat:jqnrrf5uxjhfnk3fno7lpid4ay
On splitting the Clebsch graph
1994
Indagationes mathematicae
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In this paper we show that this scheme is not the closure of any non-symmetric association scheme with three classes. ...
This implies that no primitive non-symmetric association schemes with three classes on 16 elements exist. ...
3-class association scheme). ...
doi:10.1016/0019-3577(94)90004-3
fatcat:oqcmivcbu5c7der4wurtse2zpe
Page 5356 of Mathematical Reviews Vol. , Issue 97I
[page]
1997
Mathematical Reviews
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Feasibility conditions for non-symmetric 3-class association schemes. (English summary) Discrete Math. 159 (1996), no. 1-3, 111-118. ...
Applying the feasibility conditions to Johnson schemes and a short list of other primitive symmetric two-class association schemes, they prove existence of non-symmetric three- class fission schemes. ...
On non-symmetric commutative association schemes with exactly one pair of non-symmetric relations
2006
Discrete Mathematics
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In this paper, we introduce a set of feasibility and realizability conditions for a class e symmetric association scheme to be split into a class e + 1 non-symmetric commutative association scheme. ...
By applying the feasibility and realizability conditions, we obtain a classification into six categories of the class 4 non-symmetric fission schemes of group-divisible 3-schemes. ...
Let X be a class 3 symmetric association scheme the splitting of which into a class 4 non-symmetric commutative association scheme is feasible. ...
doi:10.1016/j.disc.2006.06.005
fatcat:uij4krr2vrczdb7bontq42bgke
On Tight Euclidean 6-Designs: An Experimental Result
2011
ITB Journal of Science
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Etsuko Bannai for introducing the problem and many valuable suggestions. The author would also like to thank the referees for careful reading of the manuscript and many helpful comments. ...
(by Bannai-Damarell's criteria), or 2. the non-existence of 3-class symmetric association scheme on N 1 or N 2 points (by checking on van Dam's table), or 3. the non-existence of 3-class Q-polynomial scheme ...
Corollary 2.4 A symmetric association scheme is Q-polynomial of class 3 if and only if the Krein parameters k ij q satisfy the conditions: 3 11 0 q , 2 11 0 q , and 3 12 0 q .
2.2 Distance Sets ...
doi:10.5614/itbj.sci.2011.43.1.3
fatcat:kdaazrfobze5jhu7tpzeq4rtxm
On tight Euclidean 6-designs: an experimental result
[article]
2010
arXiv
pre-print
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A finite set X ^n with a weight function w : X ⟶_>0 is called Euclidean t-design in ^n (supported by p concentric spheres) if the following condition holds: ∑_i=1^p w(X_i)/|S_i|∫_S_i f( x)dσ_i( x) =∑_ ...
In this paper we show that for case t=6 and p=2, tight Euclidean 6-designs constructed by Bajnok is the unique configuration in ^n, for 2 ≤ n ≤ 8. ...
Etsuko Bannai for introducing the problem and many valuable suggestions. The author would also like to thank the referees for careful reading of the manuscript and many helpful comments. ...
arXiv:1012.1946v1
fatcat:ogyxsapkhfdp3ek4wbrjydgj6q
Four-class Skew-symmetric Association Schemes
[article]
2010
arXiv
pre-print
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We then determine the character tables and intersection numbers for 4-class skew-symmetric pseudocyclic association schemes, the only known examples of which are cyclotomic schemes. ...
We characterize and classify 4-class imprimitive skew-symmetric association schemes. We also prove that no 2-class Johnson scheme can admit a 4-class skew-symmetric fission scheme. ...
We are indebted to the anonymous reviewers for their thoughtful reports, and in particular, for Remark 3 and pointing out some mistakes in an early draft. K. ...
arXiv:0911.0721v2
fatcat:5qsosgra7ngkho3tzb5ng4hqda
Schur rings and non-symmetric association schemes on 64 vertices
2010
Discrete Mathematics
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In this paper we enumerate essentially all non-symmetric association schemes with three classes, less than 96 vertices and with a regular group of automorphisms. ...
In one primitive case and in one imprimitive case where no association scheme was previously known we find several new association schemes. ...
Table 1 1 Feasible parameter sets for primitive non-symmetric association schemes with three classes and less than 100 vertices. No. ...
doi:10.1016/j.disc.2010.03.002
fatcat:jpvqw3f4djeetlwlyawj3gu24e
Four-class skew-symmetric association schemes
2011
Journal of combinatorial theory. Series A
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We then determine the character tables for 4-class skew-symmetric pseudocyclic association schemes, the only known examples of which are cyclotomic schemes. ...
We characterize and classify 4-class imprimitive skew-symmetric association schemes. We also prove that none of 2-class Johnson schemes admits a 4-class skew-symmetric fission scheme. ...
We are indebted to the anonymous reviewers for their thoughtful reports, and in particular, for Remark 3 and pointing out some mistakes in an early draft. K. ...
doi:10.1016/j.jcta.2010.12.002
fatcat:dgfx5ncmirbxdfq3a6gqx2vrue
The Structure of Imprimitive Non-symmetric 3-Class Association Schemes
1996
European journal of combinatorics (Print)
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So we begin to characterize the imprimitivity of non-symmetric 3-schemes (we call an n -class association scheme an n -scheme) in terms of its parameters . ...
Here we utilize the fact that an association scheme is imprimitive if f its symmetric closure is imprimitive . The symmetric closure of a non-symmetric 3-scheme is a symmetric 2-scheme . ...
An association scheme ( X , R ) is called symmetric if all its relations are symmetric , i . e . i ϭ i R for all i ; otherwise it is called non -symmetric . Let ( X , R ) be an association scheme . ...
doi:10.1006/eujc.1996.0003
fatcat:l7n45ou5trhtbm65zgxoakr7fi
On the Godsil -- Higman necessary condition for equitable partitions of association schemes
[article]
2013
arXiv
pre-print
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Godsil derived a necessary condition for equitable partitions of association schemes and noticed that it could be used to show that certain equitable partitions do not exist. ...
In the monograph 'Association schemes', C. ...
In the paper, we assume that A is a symmetric association scheme with d classes. ...
arXiv:1306.4179v1
fatcat:rvkj63uktrfehdg2gsfb5h7nha
On few-class Q-polynomial association schemes: feasible parameters and nonexistence results
2021
Ars Mathematica Contemporanea
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We present the tables of feasible parameters of primitive 3-class Q-polynomial association schemes and 4and 5-class Q-bipartite association schemes (on up to 2800, 10000, and 50000 vertices, respectively ...
), accompanied by a number of nonexistence results for such schemes obtained by analysing triple intersection numbers of putative open cases. ...
For Q-polynomial association schemes, much less is known -see Section 3 for the feasibility conditions we have used. ...
doi:10.26493/1855-3974.2101.b76
fatcat:z2e2oqdiozao3jdhhjuwmxqgqm
Spreads in strongly regular graphs
1996
Designs, Codes and Cryptography
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Such spreads give rise to colorings meeting Hoffman's lower bound for the chromatic number and to certain imprimitive three-class association schemes. ...
We call a parameter set for a strongly regular graph feasible for a spread if it satisfies these divisibility conditions. ...
Three-Class Association Schemes Suppose [' is primitive and has a spread. ...
doi:10.1007/bf00130574
fatcat:nvwwyye5wnetncsml5mtsq36fm
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