OPTIMAL LINE PACKINGS FROM FINITE GROUP ACTIONS

We provide a general program for finding nice arrangements of points in real or complex projective space from transitive actions of finite groups. In many cases, these arrangements are optimal in the sense of maximizing the minimum distance. We introduce our program in terms of general Schurian asso...

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Bibliographic Details
Published inForum of Mathematics, Sigma Vol. 8
Main Authors IVERSON, JOSEPH W., JASPER, JOHN, MIXON, DUSTIN G.
Format Journal Article
LanguageEnglish
Published Cambridge Cambridge University Press 2020
Subjects
20B99
20C15
42C15
52C99
94C30
Optimization
Online AccessGet full text
ISSN2050-5094
2050-5094
DOI10.1017/fms.2019.48

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Summary:We provide a general program for finding nice arrangements of points in real or complex projective space from transitive actions of finite groups. In many cases, these arrangements are optimal in the sense of maximizing the minimum distance. We introduce our program in terms of general Schurian association schemes before focusing on the special case of Gelfand pairs. Notably, our program unifies a variety of existing packings with heretofore disparate constructions. In addition, we leverage our program to construct the first known infinite family of equiangular lines with Heisenberg symmetry.
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ISSN:2050-5094
2050-5094
DOI:10.1017/fms.2019.48