Real Polynomials and Combinatorial Applications

The Department of Mathematics and Statistics cordially invites you to a seminar talk by Dr. Moussa Benoumhani (University of Sharjah).

Abstract:A polynomial with positive coefficients is said to be unimodal it its coefficients form a unimodal sequence (i.e., increasing then decreasing). If the polynomial has only real zeros, this implies its unimodality. Many combinatorial sequences turn out be to unimodal. We give an overview of real polynomials (especially those with only real zeros) together with some applications in combinatorics. Some open questions and conjectures are presented. We also consider a combinatorial sequence related to counting topologies on finite spaces.

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