仿射半群提升的Yannakakis型定理
A Yannakakis-type theorem for lifts of affine semigroups
AI总结：
本文提出仿射半群提升的Yannakakis型定理，定义整数松弛矩阵，证明凸锥松弛矩阵的刻画在仿射半群中成立，并用于非负整数矩阵秩研究。
摘要：
Yannakakis定理将多面体的扩展复杂度与其松弛矩阵的非负因子分解大小联系起来，是凸集提升研究中的开创性成果。受此结果以及提升在整数规划中重要性的启发，我们证明了类似结果对凸多面锥的离散类似物——仿射半群也成立。我们定义了整数松弛矩阵和仿射半群提升的概念。我们证明，凸锥设置中松弛矩阵的许多刻画在仿射半群设置中也有类似结果。我们还展示了仿射半群的松弛矩阵如何用于获得非负整数矩阵的非负整数秩研究的新结果。
英文摘要：
Yannakakis' theorem relating the extension complexity of a polytope to the size of a nonnegative factorization of its slack matrix is a seminal result in the study of lifts of convex sets. Inspired by this result and the importance of lifts in the setting of integer programming, we show that a similar result holds for the discrete analog of convex polyhedral cones-affine semigroups. We define the notions of the integer slack matrix and a lift of an affine semigroup. We show that many of the characterizations of the slack matrix in the convex cone setting have analogous results in the affine semigroup setting. We also show how slack matrices of affine semigroups can be used to obtain new results in the study of nonnegative integer rank of nonnegative integer matrices.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
