On the Number of Combinatorial Geometries
On the Number of Combinatorial Geometries
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关于组合几何的数量
DOI：
10.1112/blms/3.1.55
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发表时间：
1971
影响因子：
0.9
通讯作者：
D. Welsh
中科院分区：
文献类型：
--
作者：
M. Piff;D. Welsh
本文的目的是证明，正如CRapo和Rota[3]所猜想的那样，n元集合上的非同构几何的数目惊人地多，实际上比文[3]中给出的估计还要多。此外，正如有限的数值证据[1]所怀疑的那样，这是通过仅考虑划分几何来实现的。这个术语是克拉波-罗塔[3]的术语。
The purpose of this note is to prove that as conjectured by Crapo and Rota [3] the number of non-isomorphic geometries on an n-element set is surprisingly large, in fact larger than the estimate as given in [3]. Moreover as suspected from the limited numerical evidence [1], this is achieved by considering partition geometries only. The terminology is that of Crapo-Rota [3].