hw1 - discrete geometry federico ardila san francisco state...

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discrete geometry san francisco state university universidad de los andes federico ardila homework one (due mon. sep. 6 (sf) or wed. sep. 8 (bog)) Note. You are strongly encouraged to work together on the homework, but you must state who you worked with. You must also write your solutions independently and in your own words. You may turn in your homework at the end of the class, or by email in a single .pdf file before midnight at discretegeometry@gmail.com. (No exceptions.) Grading. The homework is graded out of 50 points. Each problem is worth 10 points. (I know. ..) L A T E X incentive. You will receive a 10% increase on your grade if you turn in your homework as a .pdf file produced in L A T E X. (Other software doesn’t count, sorry.) I reserve the right to ask you to type up your subsequent homework in L A T E X if I cannot understand your handwriting. 1. ( f -vectors of 3-polytopes) Let v,e, and f be positive integers. Prove that there exists a polytope with v vertices, e edges, and
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