Largeness of the set of finite products in a semigroup |
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Authors: | Chase Adams III Neil Hindman Dona Strauss |
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Institution: | (1) Department of Mathematics, Howard University, Washington, DC 20059, USA;(2) Mathematics Centre, University of Hull, Hull, HU6, 7RX, UK |
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Abstract: | We investigate when the set of finite products of distinct terms of a sequence 〈x
n
〉
n=1∞ in a semigroup (S,⋅) is large in any of several standard notions of largeness. These include piecewise syndetic, central, syndetic, central*, and IP*. In the case of a “nice” sequence in (S,⋅)=(ℕ,+) one has that FS(〈x
n
〉
n=1∞) has any or all of the first three properties if and only if {x
n+1−∑
t=1
n
x
t
:n∈ℕ} is bounded from above.
N. Hindman acknowledges support received from the National Science Foundation via Grant DMS-0554803. |
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Keywords: | Piecewise syndetic Central Syndetic Central* IP* |
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