# Mathematics Colloquia and Seminars

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### Some Combinatorial Problems about Numbers

**Algebra & Discrete Mathematics**

Speaker: | Prof. Andras Sebo, CNRS, Leibniz-IMAG, Grenoble |

Location: | 693 Kerr |

Start time: | Thu, Apr 4 2002, 3:10PM |

I will present some combinatorial problems coming from graph theory or polyhedral combinatorics. Various problems find common formulations using inequalities involving congruences.

We will ask several questions and provide some answers. We ask typical combinatorial questions, which are elementary, but the answer may be difficult. For most of them I can only state conjectures or particular results, which however, have applications. Among the problems we treat the 'Lonely Runner', Hilbert bases, empty simplices and their width, and new problems with new connections. For the sake of an example here is one of the questions we will study as a particular case of inequalities about fractional parts appliable to the above mentioned problems : Given rational numbers a_1, ... , a_n with denominator D and each in the interval (0,1), moreover a number 0

Prof. Sebo will visit Davis for a month. This is the first of several talks.