Mathematical Sciences: Matrix and Combinatorial Theory

该奖项支持矩阵理论的工作。 主要研究者将寻求更好地理解（0，1）-矩阵的特征值，具有不动点性质的偏序集，横截拟阵，特别是那些出现图的双环拟阵，以及树填充问题及其与具有指定行和列和的（0，1）-矩阵的联合实现的关系。 共同首席研究员将致力于非负矩阵，M-矩阵的相关类及其推广，矩阵的缩放和矩阵的惯性理论。 稀疏矩阵分析的工作和矩阵缩放的工作应用于制造业的问题。 矩阵是一个矩形数组，其中可能有来自各种各样的环的条目。 这个领域起源于世纪，是代数的一部分。 它目前是非常活跃的，鉴于其许多应用和连接与其他部分的数学以及其他科学和技术学科。

This award supports work in matrix theory. The principal investigator will seek a better understanding of eigenvalues of (0,1)-matrices, partially ordered sets with the fixed point property, transversal matroids especially those that arise bicircular matroids of graphs, and tree-packing problems and their relation to the joint-realization of (0,1)-matrices with prescribed row and column sums. The co-principal investigator will work on non-negative matrices, the related class of M-matrices and their generalizations, on scaling of matrices and inertia theory of matrices. The work on sparse matrix analysis and the work on scaling of matrices has applications to problems in manufacturing. A matrix is a rectangular array with possible entries from a wide variety of rings. This is a field which originated in the nineteenth century as part of algebra. It is currently very active in view of its many applications and connections with other parts of mathematics as well as other scientific and technical disciplines.