Maximal Independent Generating Sets of the Symmetric Group
β Scribed by Julius Whiston
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 105 KB
- Volume
- 232
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Generalizing a theorem of Moon and Moser. we determine the maximum number of maximal independent sets in a connected graph on n vertices for n sufficiently large, e.g., n > 50. = I .32. . .). Example 1.2. Let b, = i(C,), where C,z denotes the circuit of length n. Then b, = 3, 6, = 2, b, = 5, and b,
We show that S n has at most n 6Γ11+o(1) conjugacy classes of primitive maximal subgroups. This improves an n c log 3 n bound given by Babai. We conclude that the number of conjugacy classes of maximal subgroups of S n is of the form ( 12 +o(1))n. It also follows that, for large n, S n has less than
## Abstract A maximal independent set of a graph __G__ is an independent set that is not contained properly in any other independent set of __G__. Let __i(G)__ denote the number of maximal independent sets of __G__. Here, we prove two conjectures, suggested by P. ErdΓΆs, that the maximum number of m