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<p>In this paper, we explore combinatorial properties of the posets associated with Kohnert polynomials. In particular, we determine a sufficient condition guaranteeing when such “Kohnert posets” are bounded and two necessary conditions for when they are ranked. Moreover, we apply the aforementioned conditions to find complete characterizations of when the Kohnert posets associated with Demazure characters are bounded and when they are ranked. In the case of ranked Kohnert posets associated with Demazure characters, our characterization is completely in terms of the underlying weak composition and motivates the definition of what we call “pure compositions”.</p>

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On Ranked and Bounded Kohnert Posets

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月30日

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  • Laura Colmenarejo,
  • Felix Hutchins,
  • Nicholas Mayers,
  • Etienne Phillips

摘要

In this paper, we explore combinatorial properties of the posets associated with Kohnert polynomials. In particular, we determine a sufficient condition guaranteeing when such “Kohnert posets” are bounded and two necessary conditions for when they are ranked. Moreover, we apply the aforementioned conditions to find complete characterizations of when the Kohnert posets associated with Demazure characters are bounded and when they are ranked. In the case of ranked Kohnert posets associated with Demazure characters, our characterization is completely in terms of the underlying weak composition and motivates the definition of what we call “pure compositions”.