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<p>We study lattice polytopes which arise as the convex hull of chip vectors for <i>self-reachable</i> chip configurations on a tree <i>T</i>. We show that these polytopes always have the integer decomposition property and characterize the vertex sets of these polytopes. Additionally, in the case of self-reachable configurations with the smallest possible number of chips, we show that these polytopes are unimodularly equivalent to a unit cube.</p>

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Self-Reachable Configuration Polytopes for Trees

  • 期刊论文

  • 发表日期：

    2025年5月15日

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  • Benjamin Lyons,
  • McCabe Olsen

摘要

We study lattice polytopes which arise as the convex hull of chip vectors for self-reachable chip configurations on a tree T. We show that these polytopes always have the integer decomposition property and characterize the vertex sets of these polytopes. Additionally, in the case of self-reachable configurations with the smallest possible number of chips, we show that these polytopes are unimodularly equivalent to a unit cube.