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

Date and Time: Thursday, October 05, 2006, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Torsten Mütze (TU Dresden)

Switch-Setting Games

Switch-setting games like Lights Out [1] are typically modelled as a graph, where the vertices represent switches and lamps, and the edges capture the switching rules. We generalize the concepts used for a mathematical description of Lights Out and its relatives. Our approach uses bipartite graphs and allows for the analysis of a broader class of switch-setting games, which is demonstrated at a new variant of the Lights Out puzzle. Our method exhibits full duality between switches and lamps, and we get rid of some insufficiencies inherent in the modelling with non-bipartite graphs.

We present a detailed analysis of the new Lights Out variant, formulate solvability conditions, give graphically aesthetic interpretations and discuss aspects on minimum solutions. In our study of parity domination in bipartite graphs we incorporate methods from linear algebra, automata theory and linear programming. We point out the close relations between graph theoretic terms and the language of algebra over $\mathbb{Z}_2$.

[1] http://mathworld.wolfram.com/LightsOutPuzzle.html

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

Previous talks by year:   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