V. Taranchuk

activity

20162026

most citedA New Lower Bound for van der Waerden Numbers

8 citations · 9 across the 18 of their papers we have counts for

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2 papers · 1 filter

math.CO2017

A Constructive Lower Bound on Szemerédi's Theorem

Vladislav Taranchuk

Let $r_{k} (n)$ denote the maximum cardinality of a set $A \subset {1, 2, \dots, n}$ such that $A$ does not contain a $k$ -term arithmetic progression. In this paper, we give a metho…

math.CO2017★ 8 cited

A New Lower Bound for van der Waerden Numbers

Thomas Blankenship, Jay Cummings, Vladislav Taranchuk

In this paper we prove a new recurrence relation on the van der Waerden numbers, $w (r, k)$ . In particular, if $p$ is a prime and $p \leq k$ then $w(r, k) > p \cdot \left(w\left(r - \…