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# Archive: Discrete Mathematics

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 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 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 Boris Brimkov, Rice University Boris Brimkov, Rice University Ewing 336 Title: Zero Forcing and Related Problems

Abstract: Zero forcing is a problem involving propagation in graphs, which has been introduced independently in the contexts of linear algebra, quantum control theory, graph search algorithms, and power network monitoring. This talk will survey the different origins and perspectives on zero forcing, summarize the main results in the field, and present novel structural and computational results about some of the variants of the problem. 11/15/2017 2:00:00 PM 11/15/2017 3:00:00 PM False Huda Chuangpishit, Carleton University, Canada Huda Chuangpishit, Carleton University, Canada EWG 336 TBA 11/8/2017 2:00:00 PM 11/8/2017 3:00:00 PM False