# A density version of the Carlson–Simpson theorem

Pandelis Dodos; Vassilis Kanellopoulos; Konstantinos Tyros

Journal of the European Mathematical Society (2014)

- Volume: 016, Issue: 10, page 2097-2164
- ISSN: 1435-9855

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topDodos, Pandelis, Kanellopoulos, Vassilis, and Tyros, Konstantinos. "A density version of the Carlson–Simpson theorem." Journal of the European Mathematical Society 016.10 (2014): 2097-2164. <http://eudml.org/doc/277175>.

@article{Dodos2014,

abstract = {We prove a density version of the Carlson–Simpson Theorem. Specifically we show the following. For every integer $k \ge 2$ and every set $A$ of words over $k$ satisfying $\mathrm \{lim \ sup\}_\{n\rightarrow \infty \} |A \cap [k]^n|/k^n >0$ there exist a word $c$ over $k$ and a sequence $(w_n)$ of left variable words over $k$ such that the set $\{c\}\cup \big \lbrace c^\{\UnimplementedOperator \}w_0(a_0)^\{\UnimplementedOperator \}...^\{\UnimplementedOperator \}w_n(a_n):n\in \mathbb \{N\} \text\{ and \} a_0,...,a_n\in [k]\big \rbrace $ is contained in $A$. While the result is infinite-dimensional its proof is based on an appropriate finite and quantitative version, also obtained in the paper.},

author = {Dodos, Pandelis, Kanellopoulos, Vassilis, Tyros, Konstantinos},

journal = {Journal of the European Mathematical Society},

keywords = {words; left variable words; density; words; left variable words; density},

language = {eng},

number = {10},

pages = {2097-2164},

publisher = {European Mathematical Society Publishing House},

title = {A density version of the Carlson–Simpson theorem},

url = {http://eudml.org/doc/277175},

volume = {016},

year = {2014},

}

TY - JOUR

AU - Dodos, Pandelis

AU - Kanellopoulos, Vassilis

AU - Tyros, Konstantinos

TI - A density version of the Carlson–Simpson theorem

JO - Journal of the European Mathematical Society

PY - 2014

PB - European Mathematical Society Publishing House

VL - 016

IS - 10

SP - 2097

EP - 2164

AB - We prove a density version of the Carlson–Simpson Theorem. Specifically we show the following. For every integer $k \ge 2$ and every set $A$ of words over $k$ satisfying $\mathrm {lim \ sup}_{n\rightarrow \infty } |A \cap [k]^n|/k^n >0$ there exist a word $c$ over $k$ and a sequence $(w_n)$ of left variable words over $k$ such that the set ${c}\cup \big \lbrace c^{\UnimplementedOperator }w_0(a_0)^{\UnimplementedOperator }...^{\UnimplementedOperator }w_n(a_n):n\in \mathbb {N} \text{ and } a_0,...,a_n\in [k]\big \rbrace $ is contained in $A$. While the result is infinite-dimensional its proof is based on an appropriate finite and quantitative version, also obtained in the paper.

LA - eng

KW - words; left variable words; density; words; left variable words; density

UR - http://eudml.org/doc/277175

ER -

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