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Designs in Finite Metric Spaces: A Probabilistic Approach

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-03248503
Contributor : Patrick Sol'E Connect in order to contact the contributor
Submitted on : Friday, June 18, 2021 - 12:23:13 PM
Last modification on : Tuesday, October 19, 2021 - 10:49:40 PM
Long-term archiving on: : Sunday, September 19, 2021 - 6:04:58 PM

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Minjia Shi, Olivier Rioul, Patrick Solé. Designs in Finite Metric Spaces: A Probabilistic Approach. Graphs and Combinatorics, Springer Verlag, 2021, Special Issue commemorating the 75th anniversary of E. Bannai and H. Enomoto, 37 (4), ⟨10.1007/s00373-021-02338-1⟩. ⟨hal-03248503⟩

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