发表机构
Sharif University of Technology（谢里夫理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究引入折叠代数拟阵，证明其与几乎熵拟阵为真包含关系，构造出几乎熵但非折叠代数的拟阵，还得到具有不相容特征要求的连通端口，明确了相关表示类的分离区域。
AI 中文摘要
我们引入折叠代数拟阵。在这类表示中，每个拟阵元素被替换为有限个代数量的元组，超越度经一次均匀缩放后与拟阵阵秩一致。所得类包含代数拟阵和折叠线性拟阵，且被包含在几乎熵拟阵类中，几乎熵拟阵的秩函数是缩放熵函数的极限。我们证明该包含关系是真包含。我们的主要结果涉及Gordon提出的经典秩3拟阵M(p)：对每个素数p，证明M(p)在域K上有折叠代数表示当且仅当K的特征为p。随后，我们利用保留几乎熵性的点识别构造，得到一个13元秩3 3-连通拟阵C₂,₃，它是几乎熵拟阵但非折叠代数拟阵；选择一个公共元素作为分配者，还得到一个具有不相容特征要求的12参与者连通端口。最后，我们记录了表示类间若干其他分离区域的紧凑显式见证及规模界。
英文摘要
We introduce folded-algebraic matroids. In such a representation, every matroid element is replaced by a finite tuple of algebraic quantities, and transcendence degree agrees with matroid rank after one uniform scaling. The resulting class contains both algebraic and folded-linear matroids and is contained in the class of almost-entropic matroids, whose rank functions are limits of scaled entropy functions. We prove that the latter containment is proper. Our main result concerns the classical rank-three matroids $M(p)$ of Gordon. For every prime $p$, we show that $M(p)$ has a folded-algebraic representation over a field $K$ if and only if $K$ has characteristic $p$. We then use a point-identification construction that preserves almost-entropicity to obtain a $13$-element rank-three $3$-connected matroid $C_{2,3}$ that is almost entropic but not folded algebraic. Choosing a common element as dealer also yields a connected $12$-participant port with incompatible characteristic requirements. Finally, we record compact explicit witnesses and size bounds for several other separating regions among the representation classes.
