标题： 拟模体理想的关系式 显示英文标题

标题： Syzygies of polymatroidal ideals

摘要： 我们引入了多模的洞多项式，并证明它在多模上给出了一个赋值函数。 该多项式在齐次化后的支撑仍然是一个多模。 洞多项式在多对称提升的增强$K$环中给出了一个多模的$K$理论描述。 作为应用，我们解决了两个猜想：一个是 Bandari、Bayati 和 Herzog 关于多模理想的观点，另一个是 Castillo、Cid-Ruiz、Mohammadi 和 Montaño 关于多模的莫比乌斯支撑的观点。 显示英文摘要

摘要： We introduce the cave polynomial of a polymatroid and show that it yields a valuative function on polymatroids. The support of this polynomial after homogenization is again a polymatroid. The cave polynomial gives a $K$-theoretic description of a polymatroid in the augmented $K$-ring of a multisymmetric lift. As applications, we settle two conjectures: one by Bandari, Bayati, and Herzog regarding polymatroidal ideals, and another by Castillo, Cid-Ruiz, Mohammadi, and Monta\~no regarding the M\"obius support of a polymatroid.