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<p>We adapt the vertical and horizontal insertion encodings of Cayley permutations to enumerate restricted growth functions, which are in bijection with unordered set partitions. For both insertion encodings, we fully classify the classes for which these languages are regular. For the horizontal insertion encoding, we also prove that the conditions to be regular are the same for restricted growth functions of matchings.</p>

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The Insertion Encoding of Restricted Growth Functions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月20日

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  • Christian Bean,
  • Paul C. Bell,
  • Abigail Ollson

摘要

We adapt the vertical and horizontal insertion encodings of Cayley permutations to enumerate restricted growth functions, which are in bijection with unordered set partitions. For both insertion encodings, we fully classify the classes for which these languages are regular. For the horizontal insertion encoding, we also prove that the conditions to be regular are the same for restricted growth functions of matchings.