%% @article{fds350520, Author = {Barcelo, H and Bernstein, M and Bockting-Conrad, S and McNicholas, E and Nyman, K and Viel, S}, Title = {Algebraic voting theory & representations of Sm ≀Sn }, Journal = {Advances in Applied Mathematics}, Volume = {120}, Year = {2020}, Month = {September}, Abstract = {We consider the problem of selecting an n-member committee made up of one of m candidates from each of n distinct departments. Using an algebraic approach, we analyze positional voting procedures, including the Borda count, as QSm≀Sn-module homomorphisms. In particular, we decompose the spaces of voter preferences and election results into simple QSm≀Sn-submodules and apply Schur's Lemma to determine the structure of the information lost in the voting process. We conclude with a voting paradox result, showing that for sufficiently different weighting vectors, applying the associated positional voting procedures to the same set of votes can yield vastly different election outcomes.}, Doi = {10.1016/j.aam.2020.102077}, Key = {fds350520} } @article{fds353793, Author = {Akin, V and Viel, S}, Title = {Interpreting Student Evaluations of Teaching}, Editor = {Maki, D and Bookman, J and Jacobson, M and Speer, N and Murphy, TJ}, Year = {2019}, Key = {fds353793} } @article{fds337147, Author = {Barnard, E and Meehan, E and Reading, N and Viel, S}, Title = {Universal Geometric Coefficients for the Four-Punctured Sphere}, Journal = {Annals of Combinatorics}, Volume = {22}, Number = {1}, Pages = {1-44}, Publisher = {Springer Nature}, Year = {2018}, Month = {March}, Abstract = {We construct universal geometric coefficients for the cluster algebra associated to the four-punctured sphere and obtain, as a by-product, the g-vectors of cluster variables. We also construct the rational part of the mutation fan. These constructions rely on a classification of the allowable curves (the curves which can appear in quasi-laminations). The classification allows us to prove the Null Tangle Property for the four-punctured sphere, thus adding this surface to a short list of surfaces for which this property is known. The Null Tangle Property then implies that the shear coordinates of allowable curves are the universal coefficients. We compute shear coordinates explicitly to obtain universal geometric coefficients.}, Doi = {10.1007/s00026-018-0378-0}, Key = {fds337147} } @article{fds337148, Author = {Gilbert, S and Tymoczko, J and Viel, S}, Title = {Generalized splines on arbitrary graphs}, Journal = {Pacific Journal of Mathematics}, Volume = {281}, Number = {2}, Pages = {333-364}, Publisher = {Mathematical Sciences Publishers}, Year = {2016}, Month = {January}, Abstract = {Let G be a graph whose edges are labeled by ideals of a commutative ring. We introduce a generalized spline, which is a vertex labeling of G by elements of the ring so that the difference between the labels of any two adjacent vertices lies in the corresponding edge ideal. Generalized splines arise naturally in combinatorics (algebraic splines of Billera and others) and in algebraic topology (certain equivariant cohomology rings, described by Goresky, Kottwitz, and MacPherson, among others). The central question of this paper asks when an arbitrary edge-labeled graph has nontrivial generalized splines. The answer is "always", and we prove the stronger result that the module of generalized splines contains a free submodule whose rank is the number of vertices in G. We describe the module of generalized splines when G is a tree, and give several ways to describe the ring of generalized splines as an intersection of generalized splines for simpler subgraphs of G. We also present a new tool which we call the GKM matrix, an analogue of the incidence matrix of a graph, and end with open questions.}, Doi = {10.2140/pjm.2016.281.333}, Key = {fds337148} }