Scholarlink

<p>We study the lattice of submonoids of the uniform block permutation monoid containing the symmetric group (which is its group of units). We prove that this lattice is distributive under union and intersection by relating the submonoids containing the symmetric group to downsets in a new partial order on integer partitions. Furthermore, we show that the sizes of the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="233_2025_10505_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="32" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathscr {J}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">J</mi> </math></EquationSource> </InlineEquation>-classes of the uniform block permutation monoid are sums of squares of dimensions of irreducible modules of the monoid algebra.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

The lattice of submonoids of the uniform block permutations containing the symmetric group

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年2月24日

查看全文
  • Rosa Orellana,
  • Franco Saliola,
  • Anne Schilling,
  • Mike Zabrocki

摘要

We study the lattice of submonoids of the uniform block permutation monoid containing the symmetric group (which is its group of units). We prove that this lattice is distributive under union and intersection by relating the submonoids containing the symmetric group to downsets in a new partial order on integer partitions. Furthermore, we show that the sizes of the \(\mathscr {J}\) J -classes of the uniform block permutation monoid are sums of squares of dimensions of irreducible modules of the monoid algebra.