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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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
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ISSN2050-5094
2050-5094
DOI10.1017/fms.2019.48

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Abstract 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.
AbstractList 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.
© The Author(s) 20202020The Author(s)This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.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.
ArticleNumber e6
Author IVERSON, JOSEPH W.
JASPER, JOHN
MIXON, DUSTIN G.
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Snippet 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...
© The Author(s) 20202020The Author(s)This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence...
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Title OPTIMAL LINE PACKINGS FROM FINITE GROUP ACTIONS
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