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<p>A mutation cycle is a cycle in a graph whose vertices are labeled by&#xa0;the quivers in a given mutation class and whose edges correspond to single mutations. For any fixed <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n\ge 4\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>≥</mo> <mn>4</mn> </mrow> </math></EquationSource> </InlineEquation>, we describe arbitrarily long mutation cycles involving <i>n</i>-vertex quivers. Each of these mutation cycles allows for an arbitrary choice of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\left( {\begin{array}{c}n\\ 2\end{array}}\right) \)</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close=")" open="("> <mrow> <mtable> <mtr> <mtd> <mi>n</mi> </mtd> </mtr> <mtr> <mtd> <mrow> <mrow /> <mn>2</mn> </mrow> </mtd> </mtr> </mtable> </mrow> </mfenced> </math></EquationSource> </InlineEquation> positive integer parameters. None of the mutation cycles we construct can be paved by short mutation cycles.</p>

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Long mutation cycles

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月29日

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  • Sergey Fomin,
  • Scott Neville

摘要

A mutation cycle is a cycle in a graph whose vertices are labeled by the quivers in a given mutation class and whose edges correspond to single mutations. For any fixed \(n\ge 4\) n ≥ 4 , we describe arbitrarily long mutation cycles involving n-vertex quivers. Each of these mutation cycles allows for an arbitrary choice of \(\left( {\begin{array}{c}n\\ 2\end{array}}\right) \) n 2 positive integer parameters. None of the mutation cycles we construct can be paved by short mutation cycles.