کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8904845 | 1633758 | 2018 | 24 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Upper bounds for s-distance sets and equiangular lines
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Upper bounds for s-distance sets and equiangular lines Upper bounds for s-distance sets and equiangular lines](/preview/png/8904845.png)
چکیده انگلیسی
The set of points in a metric space is called an s-distance set if pairwise distances between these points admit only s distinct values. Two-distance spherical sets with the set of scalar products {α,âα}, αâ[0,1), are called equiangular. The problem of determining the maximum size of s-distance sets in various spaces has a long history in mathematics. We suggest a new method of bounding the size of an s-distance set in compact two-point homogeneous spaces via zonal spherical functions. This method allows us to prove that the maximum size of a spherical two-distance set in Rn, nâ¥7, is n(n+1)2 with possible exceptions for some n=(2k+1)2â3, kâN. We also prove the universal upper bound â¼23na2 for equiangular sets with α=1a and, employing this bound, prove a new upper bound on the size of equiangular sets in all dimensions. Finally, we classify all equiangular sets reaching this new bound.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 330, 25 May 2018, Pages 810-833
Journal: Advances in Mathematics - Volume 330, 25 May 2018, Pages 810-833
نویسندگان
Alexey Glazyrin, Wei-Hsuan Yu,