So one basic approach in combinatorics is to investigate combinatorial objects by using linear algebraic parameters (ranks over various fields, spectrum, Smith normal forms, etc.) of their corresponding matrices. In this talk, we will look at some successful examples of this approach; some examples...
Special issue linear algebraic methods in combinatorics/graph theorydoi:10.1016/0024-3795(80)90092-0ELSEVIERLinear Algebra and its Applications
For example, it relates to sorting algorithms in computer science, rankings in the social sciences, and efficiently counting standard Young tableaux in combinatorics. A recursive formula was given in [16]. Brightwell and Winkler [12] showed that counting the number of linear extensions is #P-...
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SageMath has a wide range of capabilities, including algebraic and numerical computations, graphics, symbolic manipulation, and combinatorics. Its development is community-driven and it has been released under the GNU General Public License [89,90,91,92,93]. Remarkably, SageMath offers robust support...
The algebraic dexterity of linear programming duality led to a unified treatment of many deep theorems in graph theory and combinatorics. In this part, the last of the series on linear programming, we will see glimpses of the theory of network flows through a specific flow optimisation problem ...
Ch 18. Algebra II: Sequences & Series Ch 19. Algebra II: Combinatorics Review Ch 20. Algebra II: Calculations, Ratios,... Ch 21. Algebra II: Statistics Ch 22. Algebra II: TrigonometrySolving Systems of Linear Equations in Two Variables Using Determinants Related Study MaterialsBrowse...
The Spectral Theorem for Normal Linear Maps Appendices: Supplementary Notes on Matrices and Linear Systems The Language of Sets and Functions Summary of Algebraic Structures Encountered Some Common Math Symbols and Abbreviations Readership:Undergraduates in mathematics....
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