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Seminar Details

Ramsey Theory on Infinite Linear Orders

  • Start Date: February 12, 2025
  • Event Start Time: 12:15 PM
  • Event End Time: 1:15 PM
  • Seminar Series: Graduate Combinatorics Seminar
  • Presenter(s): Max Aires - Rutgers University
  • Event Location: Mathematics Graduate Student Lounge -- 7th Floor | Rutgers University | Hill Center | Mathematics Department
  • Event Additional Info: <p>See:&nbsp;<a href="https://sites.math.rutgers.edu/~kmg326/GCS/GCS.html">https://sites.math.rutgers.edu/~kmg326/GCS/GCS.html</a></p>
  • Presentation Type: Stand Alone Presentation
  • Abstract:

    Everyone knows (hopefully) Ramsey's Theorem that 2-colorings of infinite graphs contain monochromatic subsets. In this talk, we investigate generalizations of this fact to general linear orders. We first discuss operations on linear orders, in particular generalizing general arithmetic (and ordinal arithmetic) to the larger class of all linear orders. Now define alpha->(beta, gamma)^2 as the property that all 2-colorings of graphs on (an order) alpha contain a 0-monochromatic beta or a 1-monochromatic beta. We shall investigate this property and see a number or positive and negative results.