Han's Conjecture on Permutations

On Kummer's Conjecture

✍ M.Ram Murty; Yiannis N Petridis 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 120 KB

Kummer conjectured the asymptotic behavior of the first factor of the class number of a cyclotomic field. If we only ask for upper and lower bounds of the order of growth predicted by Kummer, then this modified Kummer conjecture is true for almost all primes.

On Nagata's Conjecture

✍ Brian Harbourne 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 119 KB

This paper gives an improved lower bound on the degrees d such that for general points p 1 p n ∈ P 2 and m > 0 there is a plane curve of degree d vanishing at each p i with multiplicity at least m.

On Thompson's Conjecture

✍ Chen Guiyun 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 148 KB

Ž . Ä < Let G be a finite group and N G s n g N G has a conjugacy class C, such < < 4 that C s n . Professor J. G. Thompson has conjectured that ''If G be a finite Ž . Ž . group with Z G s 1 and M a nonabelian simple group satisfying that N G s Ž . N M , then G ( M.'' We have proved that if M is a s

On the Thomassen's conjecture

✍ Jianping Li 📂 Article 📅 2001 🏛 John Wiley and Sons 🌐 English ⚖ 152 KB

## Abstract C. Thomassen proposed a conjecture: Let __G__ be a __k__‐connected graph with the stability number α ≥ __k__, then __G__ has a cycle __C__ containing __k__ independent vertices and all their neighbors. In this paper, we will obtain the following result: Let __G__ be a __k__‐connected gr

On Kaplansky's Fifth Conjecture

✍ Yorck Sommerhäuser 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 254 KB

We prove that the antipode of a semisimple Hopf algebra is an involution if the characteristic of the base field is very large.

On the Erd�s-S�s conjecture

✍ Wo?niak, Mariusz 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 337 KB

Erdos and Sos conjectured in 1963 that if G is a graph of order n and size e(G) with e(G) > $ n(k -I), then G contains every tree T of size k. W e present some partial results; in particular the proof of the conjecture in the case k = n -3 0 1996 John