Geodesic
Ramsay problems for spaces with symmetries
Izvestiya. Mathematics , Tome 64 (2000) no. 6, pp. 1091-1127.

Voir la notice de l'article provenant de la source Math-Net.Ru

For a wide class of spaces endowed with symmetries, the maximum size of a one-colour symmetric set existing under any colouring of the space in a given number of colours is determined. Discrete spaces (finite Abelian groups and initial segments of the positive integers) and continuous algebraic and geometric structures (a closed interval on the real line, figures of revolution, and compact Abelian groups) are investigated. 
@article{IM2_2000_64_6_a0,
     author = {T. O. Banakh and Ya. B. Vorobets and O. V. Verbitskii},
     title = {Ramsay problems for spaces with symmetries},
     journal = {Izvestiya. Mathematics },
     pages = {1091--1127},
     publisher = {mathdoc},
     volume = {64},
     number = {6},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2000_64_6_a0/}
}
TY  - JOUR
AU  - T. O. Banakh
AU  - Ya. B. Vorobets
AU  - O. V. Verbitskii
TI  - Ramsay problems for spaces with symmetries
JO  - Izvestiya. Mathematics 
PY  - 2000
SP  - 1091
EP  - 1127
VL  - 64
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2000_64_6_a0/
LA  - en
ID  - IM2_2000_64_6_a0
ER  - 
%0 Journal Article
%A T. O. Banakh
%A Ya. B. Vorobets
%A O. V. Verbitskii
%T Ramsay problems for spaces with symmetries
%J Izvestiya. Mathematics 
%D 2000
%P 1091-1127
%V 64
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2000_64_6_a0/
%G en
%F IM2_2000_64_6_a0
T. O. Banakh; Ya. B. Vorobets; O. V. Verbitskii. Ramsay problems for spaces with symmetries. Izvestiya. Mathematics , Tome 64 (2000) no. 6, pp. 1091-1127. http://geodesic.mathdoc.fr/item/IM2_2000_64_6_a0/

[1] Graham R. L., Rothschild B. L., Spencer J. H., Ramsey theory, John Wiley Sons, New York, 1980 | MR

[2] Grekhem R., Nachala teorii Ramseya, Mir, M., 1984 | MR

[3] Berlekamp E. R., “A construction of partitions which avoid long arithmetic progressions”, Canad. Math. Bull., 11 (1968), 409–414 | MR | Zbl

[4] Protasov I. V., “Asimmetrichno razlozhimye abelevy gruppy”, Matem. zametki, 59:3 (1996), 468–471 | MR | Zbl

[5] Banakh T. O., Protasov I. V., “Asimmetrichnye razbieniya abelevykh grupp”, Matem. zametki, 66:1 (1999), 10–19 | MR

[6] Banakh T. O., “Ob odnom kardinalnom gruppovom invariante, svyazannom s razbieniyami abelevykh grupp”, Matem. zametki, 64:3 (1998), 341–350 | MR | Zbl

[7] Lyumis L., Vvedenie v abstraktnyi garmonicheskii analiz, IL, M., 1956

[8] Alon N., Spencer J. H., The probabilistic method, John Wiley Sons, New York, 1992 | MR | Zbl

[9] Bernshtein S. N., Teoriya veroyatnostei, Gostekhizdat, M.–L., 1946

[10] Morris S., Dvoistvennost Pontryagina i stroenie lokalno kompaktnykh abelevykh grupp, Mir, M., 1980 | MR | Zbl

[11] Banakh T. O., Protasov I. V., “Pro simetrichnist rozfarbuvan pravilnikh mnogokutnikiv”, U sviti matematiki, 3:3 (1997), 9–15

[12] Federer G., Geometricheskaya teoriya mery, Mir, M., 1987 | MR

[13] Gallot S., Hullin D., Lafontaine J., Riemannian Geometry, Springer-Verlag, Berlin, 1993

[14] Edgar G. A., Measure, Topology, and Fractal Geometry, Springer-Verlag, Berlin, 1992 | MR | Zbl

[15] Kobayasi Sh., Gruppy preobrazovanii v differentsialnoi geometrii, Nauka, M., 1986 | MR

[16] Kobayasi Sh., Nomidzu K., Osnovy differentsialnoi geometrii, Nauka, M., 1981

[17] Engelking R., Theory of dimensions, finite and infinite, Heldermann-Verlag, Lemgo, 1995 | MR | Zbl