On a theorem of Rimhak Ree about permutations
β Scribed by Carol Tretkoff; Marvin Tretkoff
- Publisher
- Elsevier Science
- Year
- 1979
- Tongue
- English
- Weight
- 182 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We show that every group is the full automorphism group of an unordered k-relation for given k 2 2 on some suitable set. We are also concerned with the cardinality of a minimal representation with this property as a function of k.
Lawrence [2, Theorem 3] and Borodin and Kostochka [1, Lemma 2' 1 both give the same theorem about vertex colorings of graphs (Corollary 1 below). But Lawrence's proof, although powerful, is a little long, and Borodin and Kostoehka state the result without a proof.
A unified martingale approach is presented for establishing the asymptotic normality of some sequences of random variables. It is applied to the numbers of inversions, rises, and peaks, respectively, as well as the oscillation and the sum of consecutive pair products of a random permutation.