几何格的面-脊关联图的直径界
Diameter bound for facet-ridge incidence graphs of geometric lattices
AI总结：
本文研究有限几何格序复形的面-脊关联图直径问题，利用字典式剥壳证明其直径上界为秩r的组合数${r \rack 2}$，并给出界的紧性证据及说明紧性问题微妙的例子。
摘要：
本文证明了任意秩为$r$的有限几何格的序复形的面-脊关联图的直径至多为${r \brack 2}$。关键依据是一个众所周知的事实：任意有限几何格的原子的任意排序都会产生其序复形的字典式剥壳。本文还给出了一些证据表明这个界应该是紧的，同时提供了例子说明紧性问题相当微妙。
英文摘要：
This paper proves that the facet-ridge incidence graph of the order complex of any finite geometric lattice of rank $r$ has diameter at most ${r \choose 2}$. A key ingredient is the well-known fact that every ordering of the atoms of any finite geometric lattice gives rise to a lexicographic shelling of its order complex. The paper also gives results that provide some evidence that this bound ought to be sharp as well as examples indicating that the question of sharpness is quite subtle.
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。
