Mathematical Research Seminar - Archive
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31.01.2011. ob 10:00 Seminarska soba v Galebu
Predavatelj: dr. Jiangtao Shi (School of Mathematical Sciences, Peking University, China)
Title: On an inverse problem to Frobenius's theorem
Abstract: Let G be a finite group and e a positive integer dividing |G|, the order of G.
Denoting Le(G) = {x \in G| xe = 1}, Frobenius proved that |Le(G)| = ke for a
positive integer k ≥ 1. In this talk, we give a complete classification of finite groups
G with |Le(G)| ≤ 2e for every e dividing |G|.
SLIDES FROM THE TALK ARE AVAILABLE HERE: DOWNLOAD!
10.01.2011. ob 10:00 Seminarska soba v Galebu
Predavatelj: dr. Bojan Kuzma
Naslov: On conversion of permanent into determinant.
Povzetek: Though definition of permanent looks deceptively similar to determinant, the former is much harder to calculate than the later. A possible remedy is to convert a matrix such that the permanent of original matrix equals determinant of converted matrix. This conversion is given by a map on matrices. We will show that for matrices over finite fields no such bijective conversion is possible.
Povzetek: Though definition of permanent looks deceptively similar to determinant, the former is much harder to calculate than the later. A possible remedy is to convert a matrix such that the permanent of original matrix equals determinant of converted matrix. This conversion is given by a map on matrices. We will show that for matrices over finite fields no such bijective conversion is possible.
