Designs in Finite Metric Spaces: A Probabilistic Approach

A finite metric space is called here distance degree regular if its distance degree sequence is the same for every vertex. A notion of designs in such spaces is introduced that generalizes that of designs in Q -polynomial distance-regular graphs. An approximation of their cumulative distribution fun...

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Bibliographic Details
Published inGraphs and combinatorics Vol. 37; no. 5; pp. 1653 - 1667
Main Authors Shi, Minjia, Rioul, Olivier, Solé, Patrick
Format Journal Article
LanguageEnglish
Published Tokyo Springer Japan 01.09.2021
Springer Nature B.V
Springer Verlag
SeriesSpecial Issue commemorating the 75th anniversary of E. Bannai and H. Enomoto
Subjects
Approximation
Combinatorial analysis
Combinatorics
Distribution functions
Engineering Design
Infinity
Mathematical analysis
Mathematics
Mathematics and Statistics
Metric space
Original Paper
Orthogonal arrays
Polynomials
Designs
Distance-regular graphs
Orthogonal polynomials
Primary 05E35
Christoffel function
Secondary O5E20
05E24
Christoffel function AMS Math Sc. Cl. : Primary 05E35
Christoffel function Mathematics Subject Classification Primary 05E35
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Summary:A finite metric space is called here distance degree regular if its distance degree sequence is the same for every vertex. A notion of designs in such spaces is introduced that generalizes that of designs in Q -polynomial distance-regular graphs. An approximation of their cumulative distribution function, based on the notion of Christoffel function in approximation theory is given. As an application we derive limit laws on the weight distributions of binary orthogonal arrays of strength going to infinity. An analogous result for combinatorial designs of strength going to infinity is given.
ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-021-02338-1