Preprint
On the Independence Numbers of the Cyclic Van der Waerden Hypergraphs
Sep 2025
Abstract
Building upon the work of Berglund (2018), we establish a method for constructing subsetsB ⊆ ℤ_(mk)such thatBdoes not contain anyk -term cyclic arithmetic progressions modmk , wherem,k ∈ ℤ⁺withk ≥ 3 . This construction thereby provides concrete lower bounds for the maximum size of such subsets. Additionally, it allows us to tightly bound specific chromatic numbersχ(mk,k)ofℤ_(mk)and helps increase the lower bounds of certain cyclic Van der Waerden numbersW_(c)(k,r) , originally introduced by Burkert and Johnson (2011) as a way of bounding the standard Van der Waerden numbersW(k,r)from below forr ≥ 2 .
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Details
- Title
- On the Independence Numbers of the Cyclic Van der Waerden Hypergraphs
- Creators
- Benjamin Liber (Corresponding Author) - Drexel University
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991022199250304721