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Van der Waerden's Theorem and Avoidability in Words
[article]

2009
*
arXiv
*
pre-print

We consider some variations on this problem in the light of

arXiv:0812.2466v5
fatcat:7toejdgijjcflfie4wq5zhkm7e
*van**der**Waerden's**theorem*on arithmetic progressions. ...*Theorem*8 was inspired by some related empirical calculations by Richard (Yang) Peng. ... Since this is a finite coloring of the positive integers, we know by*van**der**Waerden's**theorem*that there exist n, d ≥ 1 such that Γ(n) = Γ(n + d) = . . . = Γ(n + αd). ...##
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On Applications of Van Der Waerden's Theorem

1975
*
Mathematics Magazine
*

An application of Witt's generalization of

doi:10.2307/2689695
fatcat:aw46att6svhydej2phhwko25nu
*van**der**Waerden's**theorem*. Very shortly after*van**der*Waerden published his proof in [2], A. ... ON APPLICATIONS OF*VAN**DER**WAERDEN'S**THEOREM*JOHN R. RABUNG, Randolph-Macon College 1. Equivalent versions of the*theorem*. In [1] B. ...##
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A note on van der Waerden's theorem

1982
*
Journal of combinatorial theory. Series A
*

In this note, we give a combinatorial version of the Furstenberg-Weiss topological proof of

doi:10.1016/0097-3165(82)90011-5
fatcat:3h2p7rhpg5cmzb7shfvqcsmoru
*van**der**Waerden's**theorem*. ... From this, they easily derive the following celebrated result of*van**der*Waerden:*THEOREM*(B. L.*van**der*Waerden [3] ). ...##
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On Applications of Van Der Waerden's Theorem

1975
*
Mathematics Magazine
*

An application of Witt's generalization of

doi:10.1080/0025570x.1975.11976466
fatcat:kqm2f76tybf2tg5vbjfg45nsaq
*van**der**Waerden's**theorem*. Very shortly after*van**der*Waerden published his proof in [2], A. ... ON APPLICATIONS OF*VAN**DER**WAERDEN'S**THEOREM*JOHN R. RABUNG, Randolph-Macon College 1. Equivalent versions of the*theorem*. In [1] B. ...##
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Translation invariant filters and van der Waerden's Theorem
[article]

2020
*
arXiv
*
pre-print

We present a self-contained proof of a strong version of

arXiv:1808.01500v2
fatcat:yi2my2lfdfdh3mrupnlq55z644
*van**der**Waerden's**Theorem*. ... Notice that, as a straight consequence, one obtains the following strong version of*van**der**Waerden's**Theorem*.*Theorem*3.2. ... The following objects are the main ingredient in our proof of*van**der**Waerden's**Theorem*. Definition 2.3. ...##
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Grünwald version of van der Waerden's theorem for semi-modules
[article]

2018
*
arXiv
*
pre-print

By establishing a Regional Multiple Recurrence

arXiv:1512.08695v4
fatcat:ctwcrdmznvbgdbfe7bqh5oan3a
*Theorem*for semimodules, we prove that one of the colors $j$ has the property that if $F\subseteq G$ is any finite set, then one can find some "syndetic" ... We can then obtain the following "Regional Multiple Recurrence*Theorem*" which generalizes and strengthens the classical*theorem*of Furstenberg and Weiss 1978 [18,*Theorem*1.5] that is for the invertible ... version of*van**der**Waerden's**theorem*as follows: Bergelson-Hindman*Theorem*([7, Corollary 3.2]). ...##
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A Canonical Polynomial Van der Waerden's Theorem
[article]

2020
*
arXiv
*
pre-print

We prove a canonical polynomial

arXiv:2004.07766v1
fatcat:rxrlnn4sy5g2no4flv3jmgyur4
*Van**der**Waerden's**Theorem*. More precisely, we show the following. ... Proof of the canonical*Van**Der**Waerden's**Theorem*In this section, we give a sketch of a short proof of the Canonical*Van**der**Waerden's**Theorem*. ... School A more recent and remarkable*theorem*in arithmetic Ramsey theory which once again extends*Van**der**Waerden's**Theorem*is the polynomial*Van**der**Waerden's**Theorem*, originally proved by Bergelson ...##
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Van der Waerden's Theorem and Avoidability in Words

2011
*
Integers
*

Their tool was a famous one from combinatorics: namely,

doi:10.1515/integ.2011.007
fatcat:xvk5v3hkzzhjfhcuixmoipovtm
*van**der**Waerden's**theorem*on arithmetic progressions [16] . ... Since this is a finite coloring of the positive integers, we know by*van**der**Waerden's**theorem*that there exist n, d ≥ 1 such that Γ(n) = Γ(n + d) = . . . = Γ(n + αd). ...##
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On a Variant of Van Der Waerden's Theorem

2010
*
Integers
*

Introduction A cornerstone of Ramsey theory is the

doi:10.1515/integ.2010.017
fatcat:yufmrycqrfgujlrkeakln3zluu
*theorem*of*van**der*Waerden [5] which states that for every positive integer k, there exists an integer W (k) such that any 2-coloring of {1, 2, . . ... Analogous to the*van**der*Waerden number W (k), we can define Q n (k) as the least integer for which any 2-coloring of {1, 2, . . . , Q n (k)} yields a monochromatic k-term quasi-progression of diameter ...##
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On van der Waerden's theorem on arithmetic progressions

1982
*
Journal of combinatorial theory. Series A
*

Proof of

doi:10.1016/0097-3165(82)90071-1
fatcat:mfhlyt7fnbdh5dcuv54xjbscmq
*Theorem*1. Proceed by induction on 1. For I= 0 the*theorem*is obvious. Assume that the*theorem*holds for some 12 0 and arbitrary m. By induction on m prove it for 1 + 1. ...*Theorem*1 may be viewed as the Hales-Jewett*theorem*rephrased in the language of arithmetic progressions. Thus in fact we have shown that this*theorem*may be proved using 2-colorings only. ...##
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Superfilters, Ramsey theory, and van der Waerden's Theorem

2009
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Topology and its Applications
*

Superfilters are generalized ultrafilters, which capture the underlying concept in Ramsey theoretic

doi:10.1016/j.topol.2009.04.014
fatcat:mdik7jc2wnekpdev7za2uwb6sa
*theorems*such as*van**der**Waerden's**Theorem*. ... Following Bergelson and Hindman's 1989*Theorem*, we present a new simultaneous generalization of the*theorems*of Ramsey,*van**der*Waerden, Schur, Folkman-Rado-Sanders, Rado, and others, where the colored ... Back to*van**der*Waerden Furstenberg-Weiss: AP (AP) 2 2 . AP is not even weakly Ramsey! ...##
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Variations on Van Der Waerden's and Ramsey's Theorems

1975
*
The American mathematical monthly
*

Rabung, On applications of

doi:10.1080/00029890.1975.11994010
fatcat:wbtvlvb5xna7vpbjrbqiftf7um
*van**der**Waerden's**theorem*, Math. Magazine, 48 (1975) 142-148. ... Ramsey's*Theorem*is the following.*Theorem*R. ...*Van**der**Waerden's**Theorem*The particular variation of*van**der**Waerden's**Theorem*to be presented here has been discovered independently by any number of people, but a proof of its equivalence to*van**der*...##
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Van Der Waerden's Coloring Theorem and Classical Spin Systems

1997
*
Modern physics letters B
*

We find a non-invertible matrix representation for

doi:10.1142/s0217984997001134
fatcat:bgzspey7eja3fn6hsrv2lpxyhy
*Van**der**Waerden's*colouring*theorem*for two distinct colours in a one dimensional periodic lattice. ... The authors would like to thank Sukumar Das Adhikary for introducing them to VDW*Theorem*. ... One of the many equivalent versions of*Van**der**Waerden's*Colouring*Theorem*in combinatoric number theory is 1) : Let X be a finite subset of N d . ...##
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A sharp threshold for van der Waerden's theorem in random subsets

2016
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Discrete Analysis
*

We establish sharpness for the threshold of

doi:10.19086/da.615
fatcat:tuuql42aqrhgtl2buwqfrlptmi
*van**der**Waerden's**theorem*in random subsets of $\mathbb{Z}/n\mathbb{Z}$. ... More precisely, for $k\geq 3$ and $Z\subseteq \mathbb{Z}/n\mathbb{Z}$ we say $Z$ has the*van**der*Waerden property if any two-colouring of $Z$ yields a monochromatic arithmetic progression of length $k$ ... In other words, we establish a sharp threshold for*van**der**Waerden's**theorem*for two colours in Z{nZ. ...##
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A constructive topological proof of van der Waerden's theorem

1995
*
Journal of Pure and Applied Algebra
*

The

doi:10.1016/0022-4049(94)00148-0
fatcat:m25fregb6bav7bk222auxqiqaq
*theorem*of*van**der*Waerden on arithmetical progression is a classic result in combinatorics. ... While its original proof was of combinatorial nature, it was shown by Furstenberg and Weiss that this*theorem*can be derived from topological dynamics. ... Derivation of*van**der**Waerden's**theorem*Before presenting the full derivation of*van**der**Waerden's**theorem*, we find it illuminating to show the derivation that W'(3,l) is a covering for any fixed 1, which ...
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