Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with M. Ghaffari, A. Steger, D. Steurer and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Tuesday, November 26, 2019, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Matija Bucic

Erdos-Szekeres theorem for multidimensional arrays

The classical Erdos-Szekeres theorem dating back almost a hundred years states that any sequence of (n-1)2+1 distinct real numbers contains a monotone subsequence of length n. This theorem has been generalised to higher dimensions in a variety of ways but perhaps the most natural one was proposed by Fishburn and Graham more than 25 years ago. They defined the concept of a monotone and a lex-monotone array and asked how large an array one needs in order to be able to find a monotone or a lex-monotone subarray of size n times n times ... times n. Fishburn and Graham obtained Ackerman-type bounds in both cases. We significantly improve these results. Regardless of the dimension we obtain at most a triple exponential bound in n in the monotone case and a quadruple exponential one in the lex-monotone case. This is joint work with Benny Sudakov and Tuan Tran.


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