标题： 科斯祖尔分次莫比乌斯代数与强弦图 显示英文标题

标题： Koszul Graded Möbius Algebras and Strongly Chordal Graphs

摘要： 拟梯度莫比乌斯代数是一个交换的分次代数，它编码了拟图的平坦格的组合学。 作为拟图的增强查环环的一个特殊子代数，它在最近证明多林-威尔逊顶部沉重猜想中起着重要作用。 最近，Mastroeni 和 McCullough 证明了拟图的查环环和增强查环环都是科兹尔的。 我们研究拟梯度莫比乌斯代数何时是科兹尔的。 我们根据图的性质来表征图的循环拟图的科兹尔拟梯度莫比乌斯代数。 我们的结果通过边排序给出了强弦图的新表征。 显示英文摘要

摘要： The graded M\"{o}bius algebra of a matroid is a commutative graded algebra which encodes the combinatorics of the lattice of flats of the matroid. As a special subalgebra of the augmented Chow ring of the matroid, it plays an important role in the recent proof of the Dowling-Wilson Top Heavy Conjecture. Recently, Mastroeni and McCullough proved that the Chow ring and the augmented Chow ring of a matroid are Koszul. We study when graded M\"obius algebras are Koszul. We characterize the Koszul graded M\"obius algebras of cycle matroids of graphs in terms of properties of the graphs. Our results yield a new characterization of strongly chordal graphs via edge orderings.