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# Discrete Mathematics

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Seminars will usually take place on Wednesdays,  9am - 10am in Ewing 336. Consult the schedule for more details. For more information, contact our seminar coordinator Sebasti​an Cioaba​.

 Sebastian Cioaba Sebastian Cioaba Ewing 336 Title: What keeps me up at night … or some open problems in spectral graph theory

Abstract: I will describe some open problems/conjectures related to eigenvalues of graphs. This include recent work by Aharoni, Alon and Berger on the smallest eigenvalue of K_{1,k}-free graphs, a conjecture of Dai on the second largest eigenvalue of the permutahedron and some conjectures related to the associahedron graphs time permitting. 11/29/2017 2:00:00 PM 11/29/2017 3:00:00 PM False David Chandler David Chandler EWG 336 Title: Computer assisted verification that certain polynomials are permutation Abstract: Previous computer searches suggested that certain three-term polynomials are permutation, including: $$f(x)=x^{11}(1+x^{4(q-1)}+x^{10(q-1)})$$ over $\Ff_{q^2},\ q=2^m, \ m$ not divisible by 5. Using a theorem of Steven Wang, we changed the problem to a directed graph and verified the conjecture using magma. With $q=3^m$ we also have the following polynomials over $\Ff_{q^2}$: \begin{enumerate} $x^3 (-1 - x^{q-1} + x^{4(q-1)})$, where $m$ is odd;// $x^7 ( 1 - x^{q-1} - x^{6(q-1)})$, where $m$ is even, not divisible by 6;// $x^7 (1 + x^{q-1} - x^{6(q-1)})$, where $m$ is even, not divisible by 6. \end{enumerate} 12/6/2017 2:00:00 PM 12/6/2017 3:00:00 PM False

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• Department of Mathematical Sciences
• University of Delaware
• 501 Ewing Hall
• Newark, DE 19716, USA
• Phone: 302-831-2653
• math-questions@udel.edu