Automorphic graphs and the Krein condition

1976 ◽  
Vol 5 (1) ◽  
Author(s):  
Norman Biggs
Keyword(s):  
Krein Condition

scholarly journals The Krein condition, spherical designs, Norton algebras and permutation groups

1978 ◽  
Vol 81 (1) ◽  
pp. 196-206 ◽  
Author(s):  
P.J. Cameron ◽  
J.-M. Goethals ◽  
J.J. Seidel
Keyword(s):  
Permutation Groups ◽  
Spherical Designs ◽  
Krein Condition

scholarly journals Krein Parameters of Fiber-Commutative Coherent Configurations

2020 ◽  
Vol 27 (01) ◽  
pp. 1-10
Author(s):  
Keiji Ito ◽  
Akihiro Munemasa
Keyword(s):  
Generalized Quadrangle ◽  
Coherent Configuration ◽  
Positive Semidefiniteness ◽  
The Absolute ◽  
Krein Condition ◽  
Coherent Configurations

For fiber-commutative coherent configurations, we show that Krein parameters can be defined essentially uniquely. As a consequence, the general Krein condition reduces to positive semidefiniteness of finitely many matrices determined by the parameters of a coherent configuration. We mention its implications in the coherent configuration defined by a generalized quadrangle. We also simplify the absolute bound using the matrices of Krein parameters.

scholarly journals The Krein condition, spherical designs, Norton algebras and permutation groups

1978 ◽  
Vol 81 (2) ◽  
pp. 196-206 ◽  
Author(s):  
P.J. Cameron ◽  
J.-M. Goethals ◽  
J.J. Seidel
Keyword(s):  
Permutation Groups ◽  
Spherical Designs ◽  
Krein Condition

scholarly journals Using Symbolic Computation to Prove Nonexistence of Distance-Regular Graphs

10.37236/7763 ◽  
2018 ◽  
Vol 25 (4) ◽  
Author(s):  
Janoš Vidali
Keyword(s):  
Symbolic Computation ◽  
Computer Algebra ◽  
Regular Graph ◽  
Computer Algebra System ◽  
Intersection Array ◽  
Regular Graphs ◽  
Distance Regular Graph ◽  
Triple Intersection ◽  
Distance Regular Graphs ◽  
Krein Condition

A package for the Sage computer algebra system is developed for checking feasibility of a given intersection array for a distance-regular graph. We use this tool to show that there is no distance-regular graph with intersection array$$\{(2r+1)(4r+1)(4t-1), 8r(4rt-r+2t), (r+t)(4r+1); 1, (r+t)(4r+1), 4r(2r+1)(4t-1)\}  (r, t \geq 1),$$$\{135,\! 128,\! 16; 1,\! 16,\! 120\}$, $\{234,\! 165,\! 12; 1,\! 30,\! 198\}$ or $\{55,\! 54,\! 50,\! 35,\! 10; 1,\! 5,\! 20,\! 45,\! 55\}$. In all cases, the proofs rely on equality in the Krein condition, from which triple intersection numbers are determined. Further combinatorial arguments are then used to derive nonexistence. 

scholarly journals Operators on the vanishing moments subspace and Stieltjes classes for M-indeterminate probability distributions

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Marcos López-García
Keyword(s):  
Hilbert Transform ◽  
Probability Distributions ◽  
Vanishing Moments ◽  
Content Type ◽  
Integrable Functions ◽  
Methods And Techniques ◽  
Probability Densities ◽  
Complex Integration ◽  
Krein Condition ◽  
The Hilbert Transform

PurposeIn this work the author gathers several methods and techniques to construct systematically Stieltjes classes for densities defined on R+.Design/methodology/approachThe author uses complex integration to obtain integrable functions with vanishing moments sequence, and then the author considers some operators defined on the vanishing moments subspace.FindingsThe author gather several methods and techniques to construct systematically Stieltjes classes for densities defined on R+. The author constructs explicitly Stieltjes classes with center at well-known probability densities. The author gives a lot of examples, including old cases and new ones.Originality/valueThe author computes the Hilbert transform of powers of |ln⁡x| to construct Stieltjes classes by using a recent result connecting the Krein condition and the Hilbert transform.

scholarly journals Krein Condition in Probabilistic Moment Problems

Bernoulli ◽  
2000 ◽  
Vol 6 (5) ◽  
pp. 939 ◽  
Author(s):  
Jordan Stoyanov
Keyword(s):  
Moment Problems ◽  
Krein Condition
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