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One sided ideals and Carlson's Theorem
Author(s):
Neil
Hindman;
Randall
McCutcheon
Journal:
Proc. Amer. Math. Soc.
130
(2002),
2559-2567.
MSC (1991):
Primary 05D10;
Secondary 22A15, 22A30, 54D30
Posted:
March 12, 2002
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Abstract:
Using left ideals, right ideals, and the smallest two sided ideal in a compact right topological semigroup, we derive an extension of the Main Lemma to Carlson's Theorem. This extension involves an infinite sequence of variable words over a finite alphabet, some of which are required to have the variable as the first letter and others of which are required to have the variable as the last letter.
References:
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- 2.
- T. Carlson, Some unifying principles in Ramsey Theory, Discrete Math. 68 (1988), 117-169. MR 89b:04006
- 3.
- T. Carlson and S. Simpson, A dual form of Ramsey's Theorem, Advances in Math. 53 (1984), 265-290. MR 85h:04002
- 4.
- H. Furstenberg, Recurrence in ergodic theory and combinatorial number theory, Princeton University Press, 1981. MR 82j:28010
- 5.
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- 6.
- A. Hales and R. Jewett, Regularity and positional games, Trans. Amer. Math. Soc. 106 (1963), 222-229. MR 26:1265
- 7.
- N. Hindman and R. McCutcheon, Partition theorems for left and right variable words, manuscript.
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Additional Information:
Neil
Hindman
Affiliation:
Department of Mathematics, Howard University, Washington, DC 20059
Email:
nhindman@fac.howard.edu, nhindman@aol.com
Randall
McCutcheon
Affiliation:
Department of Mathematical Sciences, University of Memphis, Memphis, Tennessee 38152
Email:
randall@msci.memphis.edu
DOI:
10.1090/S0002-9939-02-06396-7
PII:
S 0002-9939(02)06396-7
Received by editor(s):
October 16, 2000
Received by editor(s) in revised form:
April 19, 2001
Posted:
March 12, 2002
Additional Notes:
The first author acknowledges support received from the National Science Foundation (USA) via grant DMS-0070593
The second author acknowledges support received from the National Science Foundation via a post doctoral fellowship administered by the University of Maryland
Communicated by:
John R. Stembridge
Copyright of article:
Copyright
2002,
American Mathematical Society
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