The determinant and the permanent of a matrix are central characters in an endeavour to bring the powerful weapons of modern geometry to a battle in the epic war of computer science: the P vs. NP problem.
JM Landsberg has recently written a wonderful introduction to geometric complexity theory which is how the corresponding research field is called. This has inspired me to borrow some of it and write about the permanent and the determinant of a matrix.
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Being on parental leave, somewhat naturally, gave me more time to spend in the kids’ room. After a chance encounter with Mr Pythagoras there some time ago, it was now time for a scheduled meeting with Mr Euler. The configuration in the image to this post is known to young parents as an Oball. To mathematicians, it is known as the truncated icosahedron. An interesting fact is that because it is constructed entirely from pentagons and hexagons, it has to have exactly 12 pentagons. Let’s see how Mr Euler can convince us of this necessity. Continue reading →