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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.

4 votes

Local-global approach to graph theory

There are many results on locally such-and-such graphs in algebraic combinatorics. One of the first, and nicest, of them is the classification of locally Petersen graphs: J. I. Hall, Locally Petersen …
Dima Fon-Der-Flaass's user avatar
12 votes
3 answers
1k views

distance regular metric spaces

A metric space (V,d) will be called distance regular if for every distances a>0, b, c a nonnegative integer p(a,b,c) is defined, so that whenever d(B,C)=a, there are precisely p(a,b,c) points A such t …
Dima Fon-Der-Flaass's user avatar
15 votes
Accepted

Generalization of the shakehands/condom puzzle?

This problem is well-known as "glove problem" or, indeed, "condom problem". It was almost solved by Hajnal and Lovasz in 1978, with final touches put by Vardi in 1991. http://mathworld.wolfram.com/Gl …
Dima Fon-Der-Flaass's user avatar