Non-dominating Sequences of Vectors Using only Resets and Increments

Abstract

We consider sequences of vectors from ℕ ^d . Each coordinate of a vector can be reset or incremented by 1 with respect to the same coordinate of the preceding vector. We give an example of non-dominating sequence, like in Dickson’s Lemma, of length 2^2θ(n) , what matches the previously known upper bound.