On the relational complexity of a finite permutation group
On the relational complexity of a finite permutation group
复制标题
有限置换群的关系复杂度
DOI：
10.1007/s10801-015-0636-8
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发表时间：
2016
影响因子：
0.8
通讯作者：
G. Cherlin
中科院分区：
文献类型：
--
作者：
G. Cherlin
有限置换群的关系复杂度$$\rho（X，G）$$ρ（X，G）是最小的k，对于该k，该群可以被视为自然作用于关系为k元的齐次关系系统的自同构群（还给出了该定义的显式置换群理论版本）。在本原置换群的背景下，自然问题是（a）粗略估计，或（最好）在自然情况下精确值$$\rho $$ρ;和（B）粗略确定本原置换群，其中$$\rho $$ρ非常小（有界）或非常大（比次数的对数大得多）。（a）的粗略版本与（B）有关。我们的主要结果是二元（$$\rho =2$$ρ=2）本原仿射置换群的一个明确的特征。我们还计算了$${\marthm {Alt}_n$$Altn作用于k-集的精确关系复杂度，纠正了零星齐次结构中的Cherlin。在：Gelfand数学研讨会，1996年至1999年，页。15-48，Birkhäuser 2000，实施例5）。
The relational complexity $$\rho (X,G)$$ρ(X,G) of a finite permutation group is the least k for which the group can be viewed as an automorphism group acting naturally on a homogeneous relational system whose relations are k-ary (an explicit permutation group theoretic version of this definition is also given). In the context of primitive permutation groups, the natural questions are (a) rough estimates, or (preferably) precise values for $$\rho $$ρ in natural cases; and (b) a rough determination of the primitive permutation groups with $$\rho $$ρ either very small (bounded) or very large (much larger than the logarithm of the degree). The rough version of (a) is relevant to (b). Our main result is an explicit characterization of the binary ($$\rho =2$$ρ=2) primitive affine permutation groups. We also compute the precise relational complexity of $${{\mathrm{Alt}}}_n$$Altn acting on k-sets, correcting (Cherlin in Sporadic homogeneous structures. In: The Gelfand Mathematical Seminars, 1996–1999, pp. 15–48, Birkhäuser 2000, Example 5).
影响因子：
0.9
作者：
Wiscons, Joshua
通讯作者：
Wiscons, Joshua