Let F be a field, char(F) / = 2, and S β GL n (F), where n is a positive integer. In this paper we show that if for every distinct elements x, y β S, x + y is singular, then S is finite. We conjecture that this result is true if one replaces field with a division ring.
The Clique Numbers of Regular Graphs
β Scribed by Narong Punnim
- Publisher
- Springer Japan
- Year
- 2002
- Tongue
- English
- Weight
- 84 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0911-0119
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
For each natural number n, denote by G(n) the set of all numbers c such that there exists a graph with exactly c cliques (i.e., complete subgraphs) and n vertices. We prove the asymptotic estimate Ia(n)l = 0(2"n -z/5) and show that all natural numbers between n + 1 and 2 "-6"5~6 belong to G(n). Thus
In this paper, we consider total clique covers and intersection numbers on multifamilies. We determine the antichain intersection numbers of graphs in terms of total clique covers. From this result and some properties of intersection graphs on multifamilies, we determine the antichain intersection n
Denote the number of vertices of G by ]G[. A clique of graph G is a maximal complete subgraph. The density oJ(G) is the number of vertices in the largest clique of G. If Β’o(G)>~Β½ ]GI, then G has at most 2 tΒ°l-'cG) cliques. The extremal graphs are then examined as wen. ## Terminology We will be co