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- W2014778994 abstract "Base sequences of lengths <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=n plus 1> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>n + 1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=n plus 1> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>n + 1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, <italic>n</italic>, <italic>n</italic> are constructed for all decompositions of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=4 n plus 2> <mml:semantics> <mml:mrow> <mml:mn>4</mml:mn> <mml:mi>n</mml:mi> <mml:mo>+</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>4n + 2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> into four squares for <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=n equals 19 comma ellipsis comma 24> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>19</mml:mn> <mml:mo>,</mml:mo> <mml:mo>…<!-- … --></mml:mo> <mml:mo>,</mml:mo> <mml:mn>24</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>n = 19, ldots ,24</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. The construction is achieved through an algorithm which is also presented. It is proved through an exhaustive search that Turyn sequences do not exist for <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=n equals 18 comma ellipsis comma 27> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>18</mml:mn> <mml:mo>,</mml:mo> <mml:mo>…<!-- … --></mml:mo> <mml:mo>,</mml:mo> <mml:mn>27</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>n = 18, ldots ,27</mml:annotation> </mml:semantics> </mml:math> </inline-formula>; since Turyn sequences cannot exist for <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=n equals 28> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>28</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>n = 28</mml:annotation> </mml:semantics> </mml:math> </inline-formula> or 29, the first unsettled case is <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=n equals 30> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>30</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>n = 30</mml:annotation> </mml:semantics> </mml:math> </inline-formula>." @default.
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- W2014778994 date "1990-01-01" @default.
- W2014778994 modified "2023-09-26" @default.
- W2014778994 title "On base and Turyn sequences" @default.
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