On equiangular lines in 17 dimensions and the characteristic polynomial of a Seidel matrix
For e a positive integer, we find restrictions modulo 2e on the coefficients of the characteristic polynomial χS(x) of a Seidel matrix S. We show that, for a Seidel matrix of order n even (resp., odd), there are at most 2(e−2 2) (resp., 2((e−2 2)+1) possibilities for the congruence class of χS(x) mo...
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sg-ntu-dr.10356-1466792023-02-28T19:52:42Z On equiangular lines in 17 dimensions and the characteristic polynomial of a Seidel matrix Greaves, Gary Royden Watson Yatsyna, Pavlo School of Physical and Mathematical Sciences Science::Mathematics Spherical Codes Equiangular For e a positive integer, we find restrictions modulo 2e on the coefficients of the characteristic polynomial χS(x) of a Seidel matrix S. We show that, for a Seidel matrix of order n even (resp., odd), there are at most 2(e−2 2) (resp., 2((e−2 2)+1) possibilities for the congruence class of χS(x) modulo 2eZ[x]. As an application of these results we obtain an improvement to the upper bound for the number of equiangular lines in R17, that is, we reduce the known upper bound from 50 to 49. Ministry of Education (MOE) Accepted version The first author was supported by the Singapore Ministry of Education Academic Research Fund (Tier 1); grant number: RG127/16. 2021-03-04T08:37:33Z 2021-03-04T08:37:33Z 2019 Journal Article Greaves, G. R. W., & Yatsyna, P. (2019). On equiangular lines in 17 dimensions and the characteristic polynomial of a Seidel matrix. Mathematics of Computation, 88(320), 3041-3061. doi:10.1090/mcom/3433 0025-5718 https://hdl.handle.net/10356/146679 10.1090/mcom/3433 320 88 3041 3061 en RG127/16 Mathematics of Computation © 2019 American Mathematical Society. All rights reserved. This paper was published in Mathematics of Computation and is made available with permission of American Mathematical Society. application/pdf |
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Science::Mathematics Spherical Codes Equiangular |
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Science::Mathematics Spherical Codes Equiangular Greaves, Gary Royden Watson Yatsyna, Pavlo On equiangular lines in 17 dimensions and the characteristic polynomial of a Seidel matrix |
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For e a positive integer, we find restrictions modulo 2e on the coefficients of the characteristic polynomial χS(x) of a Seidel matrix S. We show that, for a Seidel matrix of order n even (resp., odd), there are at most 2(e−2 2) (resp., 2((e−2 2)+1) possibilities for the congruence class of χS(x) modulo 2eZ[x]. As an application of these results we obtain an improvement to the upper bound for the number of equiangular lines in R17, that is, we reduce the known upper bound from 50 to 49. |
| author2 |
School of Physical and Mathematical Sciences |
| author_facet |
School of Physical and Mathematical Sciences Greaves, Gary Royden Watson Yatsyna, Pavlo |
| format |
Article |
| author |
Greaves, Gary Royden Watson Yatsyna, Pavlo |
| author_sort |
Greaves, Gary Royden Watson |
| title |
On equiangular lines in 17 dimensions and the characteristic polynomial of a Seidel matrix |
| title_short |
On equiangular lines in 17 dimensions and the characteristic polynomial of a Seidel matrix |
| title_full |
On equiangular lines in 17 dimensions and the characteristic polynomial of a Seidel matrix |
| title_fullStr |
On equiangular lines in 17 dimensions and the characteristic polynomial of a Seidel matrix |
| title_full_unstemmed |
On equiangular lines in 17 dimensions and the characteristic polynomial of a Seidel matrix |
| title_sort |
on equiangular lines in 17 dimensions and the characteristic polynomial of a seidel matrix |
| publishDate |
2021 |
| url |
https://hdl.handle.net/10356/146679 |
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1759856437519974400 |