论文标题
增强伯格曼综合体的分解
Decompositions of Augmented Bergman Complexes
论文作者
论文摘要
我们研究了一个有限套件的封闭操作员的增强伯格曼综合体，该组合在适当的公寓的阶数和操作员的独立性络合物之间进行了插值。 2020年，布雷登，嗯，马瑟恩，骄傲的脚和王都表明，增强的伯格曼综合体始终是画廊连接的，最近的布洛克，凯利，凯利，莱因纳，雷纳，雷纳，雪魔，山，山，太阳，太阳，道和张通过为“ sell sell and selling of selling of sellsers of sellsers selling of sellss”，“ “基量表”炮击。 我们表明，增强的Matroid的伯格曼综合体是顶点分解的，比可壳的属性更强。我们还证明，当且仅当平底鞋（即，其非增强的伯格曼综合体）都是可壳的，并且只有当且仅当且仅当闭合操作员的增强型伯格曼综合体都是可壳的。结果，只有当它承认旗下的炮击时，就可以增强的伯格曼综合体。也许令人惊讶的是，对于基础炮击而言，这种情况并不成立：我们描述了一个封闭操作员，其增强的伯格曼综合体是可壳的，但没有炮击顺序，基地首先出现。
We study the augmented Bergman complex of a closure operator on a finite set, which interpolates between the order complex of proper flats and the independence complex of the operator. In 2020, Braden, Huh, Matherne, Proudfoot, and Wang showed that augmented Bergman complexes of matroids are always gallery-connected, and recently Bullock, Kelley, Reiner, Ren, Shemy, Shen, Sun, Tao, and Zhang strengthened "gallery-connected" to "shellable" by providing two classes of shelling orders: "flag-to-basis" shellings and "basis-to-flag" shellings. We show that augmented Bergman complexes of matroids are vertex decomposable, a stronger property than shellable. We also prove that the augmented Bergman complex of any closure operator is shellable if and only if lattice of flats (that is, its non-augmented Bergman complex) is shellable. As a consequence, an augmented Bergman complex is shellable if and only if it admits a flag-to-basis shelling. Perhaps surprisingly, the same does not hold for basis-to-flag shellings: we describe a closure operator whose augmented Bergman complex is shellable, but has no shelling order with bases appearing first.
