{"product_id":"combinatorial-convexity-9781470467098","title":"Combinatorial Convexity","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eExplores the combinatorial properties of convex sets, families of convex sets in finite dimensional Euclidean spaces, and finite points sets related to convexity. This area is classic, with theorems of Helly, Caratheodory, and Radon that go back more than a hundred years. At the same time, it is a modern and active field of research.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eThis is an elegant, well written, concise treatment of an attractive and active subject, written by an expert who has made important contributions to the area himself. I am sure this will be a successful textbook.\"\" —Noga Alon, Princeton University and Tel Aviv University\u003cbr\u003e\u003cbr\u003e\"\"I think this book is a gem.\"\" —Janos Pach, Renyi Institute of Mathematics, Budapest\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cul\u003e\n\u003cli\u003eBasic concepts\u003c\/li\u003e\n\u003cli\u003e Caratheodory's theorem\u003c\/li\u003e\n\u003cli\u003e Radon's theorem\u003c\/li\u003e\n\u003cli\u003e Topological Radon\u003c\/li\u003e\n\u003cli\u003e Tverberg's theorem\u003c\/li\u003e\n\u003cli\u003e General position\u003c\/li\u003e\n\u003cli\u003e Helly's theorem\u003c\/li\u003e\n\u003cli\u003e Applications of Helly's theorem\u003c\/li\u003e\n\u003cli\u003e Fractional Helly\u003c\/li\u003e\n\u003cli\u003e Colourful Caratheodory\u003c\/li\u003e\n\u003cli\u003e Colourful Caratheodory again\u003c\/li\u003e\n\u003cli\u003e Colourful Helly\u003c\/li\u003e\n\u003cli\u003e Tverberg's theorem again\u003c\/li\u003e\n\u003cli\u003e Colourful Tverberg theorem\u003c\/li\u003e\n\u003cli\u003e Sarkaria and Kirchberger generalized\u003c\/li\u003e\n\u003cli\u003e The Erdos-Szekers theorem\u003c\/li\u003e\n\u003cli\u003e The same type lemma\u003c\/li\u003e\n\u003cli\u003e Better bound for the Erdos-Szekeres number\u003c\/li\u003e\n\u003cli\u003e Covering number, planar case\u003c\/li\u003e\n\u003cli\u003e The stretched grid\u003c\/li\u003e\n\u003cli\u003e Covering number, general case\u003c\/li\u003e\n\u003cli\u003e Upper bound on the covering number\u003c\/li\u003e\n\u003cli\u003e The point selection theorem\u003c\/li\u003e\n\u003cli\u003e Homogeneous selection\u003c\/li\u003e\n\u003cli\u003e Missing few simplices\u003c\/li\u003e\n\u003cli\u003e Weak $\\varepsilon$-nets\u003c\/li\u003e\n\u003cli\u003e Lower bound on the size of weak $\\varepsilon$-nets\u003c\/li\u003e\n\u003cli\u003e The $(p,q)$ theorem\u003c\/li\u003e\n\u003cli\u003e The colourful $(p,q)$ theorem\u003c\/li\u003e\n\u003cli\u003e $d$-intervals\u003c\/li\u003e\n\u003cli\u003e Halving lines, havling planes\u003c\/li\u003e\n\u003cli\u003e Convex lattice sets\u003c\/li\u003e\n\u003cli\u003e Fractional Helly for convex lattice sets\u003c\/li\u003e\n\u003cli\u003e Bibliography\u003c\/li\u003e\n\u003cli\u003e Index\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"MP-AMM American Mathematical","offers":[{"title":"Default Title","offer_id":51359439814999,"sku":"9781470467098","price":43.16,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781470467098.jpg?v=1754124653","url":"https:\/\/bookcurl.com\/products\/combinatorial-convexity-9781470467098","provider":"Book Curl","version":"1.0","type":"link"}