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• W3100845880 abstract "In this paper, we consider the discrete power function associated with the sixth Painlevé equation. This function is a special solution of the so-called cross-ratio equation with a similarity constraint. We show in this paper that this system is embedded in a cubic lattice with <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mrow> <mml:mover> <mml:mi>W</mml:mi> <mml:mo stretchy=false>~</mml:mo> </mml:mover> </mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mn>3</mml:mn> <mml:msubsup> <mml:mi>A</mml:mi> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo stretchy=false>)</mml:mo> </mml:math> symmetry. By constructing the action of <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mrow> <mml:mover> <mml:mi>W</mml:mi> <mml:mo stretchy=false>~</mml:mo> </mml:mover> </mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mn>3</mml:mn> <mml:msubsup> <mml:mi>A</mml:mi> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo stretchy=false>)</mml:mo> </mml:math> as a subgroup of <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mrow> <mml:mover> <mml:mi>W</mml:mi> <mml:mo stretchy=false>~</mml:mo> </mml:mover> </mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mn>4</mml:mn> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo stretchy=false>)</mml:mo> </mml:math> , i.e. the symmetry group of P VI , we show how to relate <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mrow> <mml:mover> <mml:mi>W</mml:mi> <mml:mo stretchy=false>~</mml:mo> </mml:mover> </mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mn>4</mml:mn> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo stretchy=false>)</mml:mo> </mml:math> to the symmetry group of the lattice. Moreover, by using translations in <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mrow> <mml:mover> <mml:mi>W</mml:mi> <mml:mo stretchy=false>~</mml:mo> </mml:mover> </mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mn>3</mml:mn> <mml:msubsup> <mml:mi>A</mml:mi> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo stretchy=false>)</mml:mo> </mml:math> , we explain the odd–even structure appearing in previously known explicit formulae in terms of the τ function." @default.
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• W3100845880 date "2017-11-01" @default.
• W3100845880 modified "2023-10-17" @default.
• W3100845880 title "Geometric description of a discrete power function associated with the sixth Painlevé equation" @default.
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• W3100845880 doi "https://doi.org/10.1098/rspa.2017.0312" @default.
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