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: Thursday, January 28, 2016, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Zur Luria (ITS)

Discrepancy in high-dimensional permutations

An order-n d-dimensional permutation is a 0-1 (d+1)-dimensional array A of side length n, such that each line contains a single 1 element. Here a line is the set of elements of A obtained by fixing all but one index and letting that index vary from 1 to n. A 1-dimensional permutation is a permutation matrix, and 2-dimensional permutations are equivalent to Latin squares. We define the discrepancy of A to be the maximum over all tuples of subsets X = (X_1, ... ,X_d+1) of V of ||A(X)|-|X_1||X_2|...|X_d+1|/n|. Here A(X) counts the number of 1-elements in A in the combinatorial box X. Motivated by the expander mixing lemma, we conjecture that a typical A satisfies disc(A) < O((|X_1||X_2|...|X_d+1|)^(1/2)). A consequence of this conjecture is that the maximal volume of an empty box (for any d) is O(n^2). Using Peter Keevash's recent construction of designs, we showed that this is true in dimension 2. Joint work with Nati Linial.

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