On an invariant related to a linear inequality

Amnon Besser; Pieter Moree

doi:10.1007/BF02638383

On an invariant related to a linear inequality

Amnon Besser, Pieter Moree

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Let α = (α₁, α₂, ..., α_m) ∈ ℝ_>0^m. Let α_i,j be the vector obtained from α on deleting the entries α_i and α_j. We investigate some invariants and near invariants related to the solutions ∈ ∈ {± 1}^m-2 of the linear inequality |α_i - α_j| < 〈 ∈, α_i,j 〉 < α_i + α_j, where 〈, 〉 denotes the usual inner product. One of our methods relates, by the use of Rademacher functions, integrals involving products of trigonometric functions to these quantities.

Original language	English
Pages (from-to)	463-471
Number of pages	9
Journal	Archiv der Mathematik
Volume	79
Issue number	6
DOIs	https://doi.org/10.1007/BF02638383
State	Published - 1 Dec 2002

ASJC Scopus subject areas

General Mathematics

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abstract = "Let α = (α1, α2, ..., αm) ∈ ℝ>0m. Let αi,j be the vector obtained from α on deleting the entries αi and αj. We investigate some invariants and near invariants related to the solutions ∈ ∈ \{± 1\}m-2 of the linear inequality |αi - αj| < 〈 ∈, αi,j 〉 < αi + αj, where 〈, 〉 denotes the usual inner product. One of our methods relates, by the use of Rademacher functions, integrals involving products of trigonometric functions to these quantities.",

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T1 - On an invariant related to a linear inequality

AU - Besser, Amnon

AU - Moree, Pieter

PY - 2002/12/1

Y1 - 2002/12/1

N2 - Let α = (α1, α2, ..., αm) ∈ ℝ>0m. Let αi,j be the vector obtained from α on deleting the entries αi and αj. We investigate some invariants and near invariants related to the solutions ∈ ∈ {± 1}m-2 of the linear inequality |αi - αj| < 〈 ∈, αi,j 〉 < αi + αj, where 〈, 〉 denotes the usual inner product. One of our methods relates, by the use of Rademacher functions, integrals involving products of trigonometric functions to these quantities.

AB - Let α = (α1, α2, ..., αm) ∈ ℝ>0m. Let αi,j be the vector obtained from α on deleting the entries αi and αj. We investigate some invariants and near invariants related to the solutions ∈ ∈ {± 1}m-2 of the linear inequality |αi - αj| < 〈 ∈, αi,j 〉 < αi + αj, where 〈, 〉 denotes the usual inner product. One of our methods relates, by the use of Rademacher functions, integrals involving products of trigonometric functions to these quantities.

UR - https://www.scopus.com/pages/publications/0036998447

U2 - 10.1007/BF02638383

DO - 10.1007/BF02638383

M3 - Article

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SN - 0003-889X

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SP - 463

EP - 471

JO - Archiv der Mathematik

JF - Archiv der Mathematik

IS - 6

ER -

On an invariant related to a linear inequality

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