For computations with coherent configurations

Faradžev, I. A.; Klin, Mikhail

doi:10.1145/120694.120726

Cited by 27 publications

(23 citation statements)

References 7 publications

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“…We also would like to study the relationship pointed by the Galois correspondence studied in [11] and the corresponding ideals.…”

Section: Discussionmentioning

confidence: 99%

“…Examples in the paper are teaching hints for the better comprehension of the paper, and indeed all of them can be solved by hand computation by those readers with background in algebraic combinatorics. The approach in this paper is a computational one, as a final remark to this introduction, we point that some other computational approaches can be found in [11] motivated by the works in [10,12].…”

Section: Overview and Backgroundmentioning

confidence: 99%

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Properties of Commutative Association Schemes Derived by FGLM Techniques

Martı́nez-Moro¹

2002

Int. J. Algebra Comput.

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Association schemes are combinatorial objects that allow us solve problems in several branches of mathematics. They have been used in the study of permutation groups and graphs and also in the design of experiments, coding theory, partition designs etc. In this paper we show some techniques for computing properties of association schemes. The main framework arises from the fact that we can characterize completely the Bose-Mesner algebra in terms of a zero-dimensional ideal. A Gröbner basis of this ideal can be easily derived without the use of Buchberger algorithm in an efficient way. From this statement, some nice relations arise between the treatment of zero-dimensional ideals by reordering techniques (FGLM techniques) and some properties of the schemes such as P-polynomiality, and minimal generators of the algebra.

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“…We also would like to study the relationship pointed by the Galois correspondence studied in [11] and the corresponding ideals.…”

Section: Discussionmentioning

confidence: 99%

Section: Overview and Backgroundmentioning

confidence: 99%

Properties of Commutative Association Schemes Derived by FGLM Techniques

Martı́nez-Moro¹

2002

Int. J. Algebra Comput.

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“…In closing, we wish to acknowledge the crucial role played in our research by computer algebra packages, especially GAP [23], COCO [7] and COCO-II.…”

Section: Introductionmentioning

confidence: 99%

On the existence of self-complementary and non-self-complementary strongly regular graphs with Paley parameters

2015

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For p an odd prime, let Ap be the complete classical affine association scheme whose associate classes correspond to parallel classes of lines in the classical affine plane AG(2, p). It is known that Ap is an amorphic association scheme. We investigate rank 3 fusion schemes of Ap whose basis graphs have the same parameters as the Paley graphs P (p 2 ). In contrast to the Paley graphs, the great majority of graphs we detect are non-self-complementary and non-Schurian. In particular, existence of non-self-complementary graphs with Paley parameters is established for p ≥ 17, with an analogous existence result for non-Schurian such graphs when p ≥ 11. We demonstrate that the number of self-complementary and non-self-complementary strongly regular graphs with Paley parameters grows rapidly as p → ∞.

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“…Many of the presented results rely on the essential use of computer packages and separate programs, such as [29], [35], [100], [78]. The recent paper [71] provides a reasonable discussion of the abilities of computer algebra experimentation in algebraic graph theory.…”

Section: Introductionmentioning

confidence: 99%

A new construction of antipodal distance regular covers of complete graphs through the use of Godsil-Hensel matrices

Klin

Pech²

2011

Ars Math. Contemp.

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New constructions of regular distance regular antipodal covers (in the sense of GodsilHensel) of complete graphs K n are presented. The main source of these constructions are skew generalized Hadamard matrices. It is described how to produce such a matrix of order n 2 over a group T from an arbitrary given generalized Hadamard matrix of order n over the same group T . Further, a new regular cover of K 45 on 135 vertices is produced with the aid of a decoration of the alternating group A 6 .

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For computations with coherent configurations

Cited by 27 publications

References 7 publications

Properties of Commutative Association Schemes Derived by FGLM Techniques

Properties of Commutative Association Schemes Derived by FGLM Techniques

On the existence of self-complementary and non-self-complementary strongly regular graphs with Paley parameters

A new construction of antipodal distance regular covers of complete graphs through the use of Godsil-Hensel matrices

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