Geodesic
On Free Semigroups and Ramsey Numbers
Canadian mathematical bulletin, Tome 17 (1974) no. 2, pp. 229-232

Voir la notice de l'article provenant de la source Cambridge University Press

If the length of a word w in a free semigroup F(X) satisfies , then for every partition of F(X) into k classes, w has n consecutive factors of length ≥p in the same class. As a consequence, the diagonal Ramsey numbers R(pn+1, p+1, k) have 1+pnk as lower bound. 
Lallement, Gerard. On Free Semigroups and Ramsey Numbers. Canadian mathematical bulletin, Tome 17 (1974) no. 2, pp. 229-232. doi: 10.4153/CMB-1974-045-5
@article{10_4153_CMB_1974_045_5,
     author = {Lallement, Gerard},
     title = {On {Free} {Semigroups} and {Ramsey} {Numbers}},
     journal = {Canadian mathematical bulletin},
     pages = {229--232},
     year = {1974},
     volume = {17},
     number = {2},
     doi = {10.4153/CMB-1974-045-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1974-045-5/}
}
TY  - JOUR
AU  - Lallement, Gerard
TI  - On Free Semigroups and Ramsey Numbers
JO  - Canadian mathematical bulletin
PY  - 1974
SP  - 229
EP  - 232
VL  - 17
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1974-045-5/
DO  - 10.4153/CMB-1974-045-5
ID  - 10_4153_CMB_1974_045_5
ER  - 
%0 Journal Article
%A Lallement, Gerard
%T On Free Semigroups and Ramsey Numbers
%J Canadian mathematical bulletin
%D 1974
%P 229-232
%V 17
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1974-045-5/
%R 10.4153/CMB-1974-045-5
%F 10_4153_CMB_1974_045_5

[1] 1. Chvatal, V., Hypergraphs and Ramseyian theorems, Proc. Amer. Math. Soc. 27, (1971), 434-440. Google Scholar

[2] 2. Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Vol. II, 1967, Amer. Math. Soc, Providence, R.I. Google Scholar

[3] 3. Erdös, P., Some remarks on the theory of graphs, Bull. Amer. Math. Soc. 53, 1947, 292-294. Google Scholar

[4] 4. Frasnay, C., Quelques problèmes combinatoires concernant les ordres totaux et les relations monomorphes, Ann. Inst. Fourier, Grenoble, 15, 1965, 415-524. Google Scholar

[5] 5. Ginsburg, S., The mathematical theory of context-free languages, 1966, McGraw-Hill. Google Scholar

[6] 6. Giraud, G. R., Une généralisation des nomblres et de Vinégalité de Schur, C.R. Acad. Se. Paris, t. 266 (1968), 437-440. Google Scholar

[7] 7. Greenwood, R. E. and Gleason, A. M., Combinatorial relations and chromatic graphs, Can. Journ. Math., 7, 1955, 1-7. Google Scholar

[8] 8. Hell, P., Ramsey Numbers, M.Sc. thesis, McMaster University, 1969. Google Scholar

[9] 9. Justin, J., Généralisation du théorème de Van der Waerden sur les semi-groupes répétitifs, J. Combinatorial Theory (A) 12, (1972), 357-367. Google Scholar

[10] 10. Ryser, H. J., Combinatorial mathematics, 1963, Cams Math. Monographs number 14. Google Scholar

[11] 11. Schützenberger, M. P., Quelques problèmes combinatoires de la théorie des automates, Cours de l’Institut de Programmation 1966–1967 rédigé par J. F. Perrot. Google Scholar

Cité par Sources :