Publications

2024

1. Sem. Loth. Comb.

   Geometry of c-matrices for mutation-cyclic-rank-3 quiver

   Kyungyong Lee Tucker J. Ervin, and Son D. Nguyen

   2024

   Abs Bib PDF

   @article{nguyen2024make,
     title = {Geometry of c-matrices for mutation-cyclic-rank-3 quiver},
     author = {Tucker J. Ervin, Blake Jackson, Kyungyong Lee and Nguyen, Son D.},
     journal = {},
     year = {2024}
   }

2022

1. JOA

   A proof of Lee-Lee’s conjecture about geometry of rigid modules

   Son D. Nguyen

   https://www.sciencedirect.com/science/article/abs/pii/S0021869322004045, 2022

   Abs Bib PDF

   This paper proves Lee-Lee’s conjecture that establishes a coincidence between the set of associated roots of non-self-intersecting curves in an n-punctured disc and the set of real Schur roots of acyclic (valued) quivers with n vertices.

   @article{nguyen2022make,
     title = {A proof of Lee-Lee’s conjecture about geometry of rigid modules},
     author = {Nguyen, Son D.},
     journal = {https://www.sciencedirect.com/science/article/abs/pii/S0021869322004045},
     year = {2022}
   }

2. Sem. Loth. Comb.

   Permutations whose reverse shares the same recording tableau in the RSK correspondence

   https://arxiv.org/abs/2108.08657, 2022

   Abs Bib PDF

   The RSK correspondence is a bijection between permutations and pairs of standard Young tableaux with identical shape, where the tableaux are commonly denoted P (insertion) and Q (recording).

   @article{nguyen2022makf,
     title = {Permutations whose reverse shares the same recording tableau in the RSK correspondence},
     author = {},
     year = {2022}
   }

2018

1. arxiv

   Constrained Fermat,Torricelli,Weber problem in real HilbertSpaces

   Son D. Nguyen

   https://arxiv.org/abs/2108.08657, 2018

   Abs Bib PDF

   The Fermat-Weber location problem requires finding a point in Rn that minimizes the sum of weighted Euclidean distances to m given points. An iterative solution method for this problem was first introduced by E. Weiszfeld in 1937. Global convergence of Weiszfeld’s algorithm was proven by W. Kuhn in 1973. This paper studies Fermat-Weber location problems with closed convex constraint sets in real Hilbert spaces. In section two, we show that existence and uniqueness of solutions of the problems. Moreover, the solution is stable with respect to the perturbation of the m anchor points. In the section three, we extend Weiszfeld’s algorithm by adding a projection on the constraint set. The convergence of the sequence generated by the method to the optimal solution of the problem is proved.

   @article{nguyen2018make,
     title = {Constrained Fermat,Torricelli,Weber problem in real HilbertSpaces},
     author = {Nguyen, Son D.},
     year = {2018}
   }