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<p>We prove that given a fixed finite tree <i>P</i>, almost all trees contain <i>P</i> as a subtree. Moreover, the inclusion can be made so that it induces an embedding of the corresponding (quantum) automorphism groups, thereby providing generic properties of the latter.</p>

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Patterns in trees and quantum automorphism groups

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月26日

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  • Lucas Alger,
  • Julie Capron,
  • Félix de la Salle

摘要

We prove that given a fixed finite tree P, almost all trees contain P as a subtree. Moreover, the inclusion can be made so that it induces an embedding of the corresponding (quantum) automorphism groups, thereby providing generic properties of the latter.