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 A. Steger, D. Steurer and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Tuesday, November 24, 2015, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Christian Elsholtz (TU Graz)

Hilbert cubes in arithmetic sets - or the complexity of squares

A Hilbert cube of dimension d is an iterated sumset H=a_0+{0,a_1}+ ... + {0, a_d}. Using such a cube one could store up to 2^d elements of the cube just by storing the d+1 base elements.

In this talk we prove an upper bound of d=O(log log N) on the maximal dimension d of the set of integer squares less than N. (Related results are possible, e.g. for k-th powers, pure powers, powerful numbers).

The proof combines methods from number theory and combinatorics.

Upcoming talks     |     All previous talks     |     Talks by speaker     |     Upcoming talks in iCal format (beta version!)

Previous talks by year:   2024  2023  2022  2021  2020  2019  2018  2017  2016  2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  1998  1997  1996  

Information for students and suggested topics for student talks

Automatic MiSe System Software Version 1.4803M   |   admin login