Math 108 Notes: Combinatorics
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Hopf Algebras in Combinatorics
Certain Hopf algebras arise in combinatorics because they have bases naturally parametrized by combinatorial objects (partitions, compositions, permutations, tableaux, graphs, trees, posets, polytopes, etc). The rigidity in the structure of a Hopf algebra can lead to enlightening proofs, and many interesting invariants of combinatorial objects turn out to be evaluations of Hopf morphisms. These...
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These are rather condensed notes, not really proofread or edited, presenting key definitions and results of the course that I taught in Winter 2010 term. Problems marked by ◦ are easy and basic, problems marked by ∗ may be difficult. Typeset by AMS-TEX 1
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A typical result in (additive) Ramsey theory takes the following form: if N (or {1, . . . , N} with N sufficiently large) is partitioned into finitely many classes, then at least one of these classes will contain contain a specific arithmetic structure (e.g. an arithmetic progression). The simplest example of such a result is the pigeonhole principle and one can view Ramsey theory as the study ...
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Given a bipartite graph, the bipartite global edge-connectivity aug-mentation problem consists of finding a minimum cardinality edge setwhose addition results in a bipartite k-edge-connected graph. A min-imax theorem and some applications will be presented. This part ofthe talk is based on [1].I will also mention some preliminary results from [2] concerning thelocal ...
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تاریخ انتشار 2016