Monochromatic non-commuting products
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910436637540352 |
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| author | Bowen, Matt |
| author_facet | Bowen, Matt |
| contents | We show that a finite coloring of an amenable group contains `many' monochromatic sets of the form $\{x,y,xy,yx\},$ and natural extensions with more variables. This gives the first combinatorial proof and extensions of Bergelson and McCutcheon's non-commutative Schur theorem. Our main new tool is the introduction of what we call `quasirandom colorings,' a condition that is automatically satisfied by colorings of quasirandom groups, and a reduction to this case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03772 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Monochromatic non-commuting products Bowen, Matt Combinatorics Dynamical Systems Number Theory 05D10 43A07 37B20 54D80 We show that a finite coloring of an amenable group contains `many' monochromatic sets of the form $\{x,y,xy,yx\},$ and natural extensions with more variables. This gives the first combinatorial proof and extensions of Bergelson and McCutcheon's non-commutative Schur theorem. Our main new tool is the introduction of what we call `quasirandom colorings,' a condition that is automatically satisfied by colorings of quasirandom groups, and a reduction to this case. |
| title | Monochromatic non-commuting products |
| topic | Combinatorics Dynamical Systems Number Theory 05D10 43A07 37B20 54D80 |
| url | https://arxiv.org/abs/2405.03772 |