Geodesic
A Ramsey algebraic study of matrices
Algebra and discrete mathematics, Tome 27 (2019) no. 1, pp. 85-98.

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

The notion of a topological Ramsey space was introduced by Carlson some 30 years ago. Studying the topological Ramsey space of variable words, Carlson was able to derive many classical combinatorial results in a unifying manner. For the class of spaces generated by algebras, Carlson had suggested that one should attempt a purely combinatorial approach to the study. This approach was later formulated and named Ramsey algebra. In this paper, we continue to look at heterogeneous Ramsey algebras, mainly characterizing various Ramsey algebras involving matrices.
Keywords: Ramsey algebra, Ramsey space, Ramsey theory, Hindman's theorem
Mots-clés : matrices. 
@article{ADM_2019_27_1_a9,
     author = {Zu Yao Teoh and Wen Chean Teh},
     title = {A {Ramsey} algebraic study of matrices},
     journal = {Algebra and discrete mathematics},
     pages = {85--98},
     publisher = {mathdoc},
     volume = {27},
     number = {1},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2019_27_1_a9/}
}
TY  - JOUR
AU  - Zu Yao Teoh
AU  - Wen Chean Teh
TI  - A Ramsey algebraic study of matrices
JO  - Algebra and discrete mathematics
PY  - 2019
SP  - 85
EP  - 98
VL  - 27
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2019_27_1_a9/
LA  - en
ID  - ADM_2019_27_1_a9
ER  - 
%0 Journal Article
%A Zu Yao Teoh
%A Wen Chean Teh
%T A Ramsey algebraic study of matrices
%J Algebra and discrete mathematics
%D 2019
%P 85-98
%V 27
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2019_27_1_a9/
%G en
%F ADM_2019_27_1_a9
Zu Yao Teoh; Wen Chean Teh. A Ramsey algebraic study of matrices. Algebra and discrete mathematics, Tome 27 (2019) no. 1, pp. 85-98. http://geodesic.mathdoc.fr/item/ADM_2019_27_1_a9/

[1] Garrett Birkhoff, John D. Lipson, “Heterogeneous algebras”, J. Comb. Theory, 8:1 (1970), 115–133 | DOI | MR

[2] Timothy J. Carlson, “Some unifying principles in Ramsey theory”, Discrete Math., 68:2 (1988), 117–169 | MR | Zbl

[3] Eric Ellentuck, “A new proof that analytic sets are Ramsey”, J. Symb. Log., 39:01 (1974), 163–165 | DOI | MR

[4] Neil Hindman, “Finite sums from sequences within cells of a partition of $N$”, J. Comb. Theory, Series A, 17 (1974), 1–11 | MR | Zbl

[5] Wen Chean Teh, “Ramsey algebras”, J. Math. Log., 16:2 (2016), 16 pp. | MR

[6] Wen Chean Teh, Ramsey algebras and Ramsey spaces, PhD Thesis, The Ohio State University, 2003

[7] Wen Chean Teh, “Ramsey algebras and formal orderly terms”, Notre Dame J. Form. Log., 58:1 (2017), 115–125 | MR | Zbl

[8] Wen Chean Teh, “Ramsey algebras and strongly reductible ultrafilters”, Bull. Malays. Math. Sci. Soc., 37:4 (2014), 931–938 | MR | Zbl

[9] Wen Chean Teh, “Ramsey algebras and the existence of idempotent ultrafilters”, Arch. Math. Log., 55:3 (2016), 475–491 | MR | Zbl

[10] Zu Yao Teoh, Wen Chean Teh, A Ramsey algebraic study of matrices, arXiv: 1706.00565 [math.LO] | MR

[11] Zu Yao Teoh, Wen Chean Teh, “Heterogeneous Ramsey Algebras and Classification of Ramsey Vector Spaces”, Bull. Malays. Math. Sci. Soc., 41:2 (2018), 1011–1028 | MR | Zbl

[12] Wen Chean Teh, Zu Yao Teoh, “Ramsey Orderly Algebra”, East-West J. Math., 19:1 (2017), 89–102 | MR

[13] Stevo Todorcevic, Introduction to Ramsey spaces, Ann. of Math. Studies, 174, Princeton University Press, Princeton, NJ, 2010 | MR