0000000000180103

AUTHOR

Mario Osvin Pavčević

showing 3 related works from this author

Some new Hadamard designs with 79 points admitting automorphisms of order 13 and 19

2001

Abstract We have proved that there exists at least 2091 mutually nonisomorphic symmetric (79,39,19)-designs. In particular, 1896 of them admit an action of the nonabelian group of order 57, and an additional 194 an action of the nonabelian group of order 39.

Group (mathematics)Existential quantificationOrbit structureAutomorphismAction (physics)Automorphism groupOrbit structureTheoretical Computer ScienceCombinatoricsHadamard transformHadamard design; Automorphism group; Tactical decomposition; Orbit structureHadamard designDiscrete Mathematics and CombinatoricsOrder (group theory)Tactical decompositionHadamard matrixMathematicsDiscrete Mathematics
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Symmetric (79, 27, 9)-designs Admitting a Faithful Action of a Frobenius Group of Order 39

1997

AbstractIn this paper we present the classification of symmetric designs with parameters (79, 27, 9) on which a non-abelian group of order 39 acts faithfully. In particular, we show that such a group acts semi-standardly with 7 orbits. Using the method of tactical decompositions, we are able to construct exactly 1320 non-isomorphic designs. The orders of the full automorphism groups of these designs all divide 8 · 3 · 13.

Discrete mathematicsKlein four-groupG-moduleQuaternion groupAlternating groupOuter automorphism groupGroup representationsymmetric design; Frobenius group; orbit structureTheoretical Computer ScienceCombinatoricsComputational Theory and MathematicsSymmetric groupDiscrete Mathematics and CombinatoricsGeometry and TopologyFrobenius groupMathematicsEuropean Journal of Combinatorics
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A Series of Hadamard Designs with Large Automorphism Groups

2000

Abstract Whilst studying a certain symmetric (99, 49, 24)-design acted upon by a Frobenius group of order 21, it became clear that the design would be a member of an infinite series of symmetric (2q2 + 1, q2, (q2 − 1)/2)-designs for odd prime powers q. In this note, we present the definition of the series and give some information about the automorphism groups of its members.

incidence matrixAlgebra and Number TheoryOuter automorphism groupAlternating groupAutomorphismCombinatoricsInner automorphismSymmetric groupOrder (group theory)symmetric design; Hadamard matrix; incidence matrix; orbit structureHadamard matrixFrobenius grouporbit structuresymmetric designHadamard matrixMathematicsJournal of Algebra
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