Filters








56,885 Hits in 4.1 sec

Feasibility conditions for non-symmetric 3-class association schemes

R.W. Goldbach, H.L. Claasen
1996 Discrete Mathematics  
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

Sung Y Song
1995 Journal of combinatorial theory. Series A  
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]

Leif K. Jørgensen
2009 Algorithmic Algebraic Combinatorics and Gröbner Bases  
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

R.W. Goldbach, H.L. Claasen
1994 Indagationes mathematicae  
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  
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

G.L. Chia, W.K. Kok
2006 Discrete Mathematics  
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

Djoko Suprijanto
2011 ITB Journal of Science  
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]

Djoko Suprijanto
2010 arXiv   pre-print
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]

Jianmin Ma, Kaishun Wang
2010 arXiv   pre-print
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

Leif K. Jørgensen
2010 Discrete Mathematics  
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

Jianmin Ma, Kaishun Wang
2011 Journal of combinatorial theory. Series A  
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

R.W. Goldbach, H.L. Claasen
1996 European journal of combinatorics (Print)  
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]

Alexander L. Gavrilyuk, Ivan Yu. Mogilnykh
2013 arXiv   pre-print
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

Alexander L. Gavrilyuk, Janoš Vidali, Jason S. Williford
2021 Ars Mathematica Contemporanea  
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

Willem H. Haemers, Vladimir D. Tonchev
1996 Designs, Codes and Cryptography  
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
« Previous Showing results 1 — 15 out of 56,885 results