Additive Combinatorics - Bajnok, Bela

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Résumé :
Additive Combinatorics: A Menu of Research Problems is the first book of its kind in aims and scope: it provides readers with an opportunity to actively explore the relatively new field of additive combinatorics. The author has written it specifically for students of any background and proficiency level, from beginners to advanced researchers....

Sommaire:

Ingredients.Number theory. Divisibility of integers. Congruences.The Fundamental Theorem of Number Theory. Multiplicative number theory. Additive number theory. Combinatorics.Basic enumeration principles.Counting lists, sequences, sets, and multisets.Binomial coefficients and Pascal?s Triangle. Some recurrence relations. The integer lattice and its layers. Group theory. Finite abelian groups. Group isomorphisms. The Fundamental Theorem of Finite Abelian Groups. Subgroups and cosets. Subgroups generated by subsets. Sumsets. Appetizers. Spherical designs. Caps, centroids, and the game SET. How many elements does it take to span a group? In pursuit of perfection.The declaration of independence. Sides. Auxiliary functions. Entrees. Maximum sumset size. Spanning set. Sidon sets. Minimum sumset size. The critical number. Zero-sum-free sets. Sum-free sets. Pudding. Proof of Propositions and Theorems