布尔格的一些商是对称链序
组合数学
2011-08-29 v2
摘要
R. Canfield 猜想：对于布尔格 B(n) 的自同构群（可视为对称群 S(n)）的所有子群 G，商序 B(n)/G 都是对称链序。我们给出了 K. K. Jordan 的一个结果的推广的直接证明：即当 G 由不相交循环的幂生成时，B(n)/G 是 SCO。Greene 和 Kleitman 的对称链分解为这些商的分割提供了基础。
引用
@article{arxiv.1107.1098,
title = {Some Quotients of the Boolean Lattice are Symmetric Chain Orders},
author = {Dwight Duffus and Jeremy McKibben-Sanders and Kyle Thayer},
journal= {arXiv preprint arXiv:1107.1098},
year = {2011}
}
备注
The significant changes from the first version are: inclusion of Theorem 3 and Corollary 1, with the proof of the former in Section 5. Small corrections and rewordings have been done as well