University of Birmingham > Talks@bham > Combinatorics and Probability seminar > Monochromatic Sums and Products over the Rationals

Monochromatic Sums and Products over the Rationals

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If you have a question about this talk, please contact Dr Richard Mycroft.

Hindman’s Theorem states that whenever the natural numbers are finitely coloured there exists an infinite sequence all of those finite sums are the same colour. By considering just powers of 2, this immediately implies the corresponding result for products: whenever the naturals are finitely coloured there exists a sequence all of whose products are the same colour.

But what happens if we ask for both the sums and the products to all have the same colour? It turns out that this is not true: it has been known since the 1970s that there is a finite colouring of the naturals for which no infinite sequence has the set of all of its sums and products monochromatic.

In this talk we will investigate what happens to this question if we move from the naturals to a larger space such as the dyadic rationals, the rationals, or even the reals.

Joint work with Neil Hindman and Imre Leader.

This talk is part of the Combinatorics and Probability seminar series.

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