On edge-ordered Ramsey numbers of hypergraphs

Source abstract

For an integer $h\geq2$, an edge-ordered $h$-uniform hypergraph $H^ 0$ is a constant. For fixed $h\geq3$ and $q\geq2$, this shows that prescribing the hyperedge order does not require an increase in the tower height of the classical upper bound. It also settles a problem posed by Fox and Li (2020), and for $h=2$ gives the bound $2^{O(n^4\log n)}$, improving their bounds for every fixed $q \geq 3$.