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A
Additive combinatorics
Algebraic combinatorics
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Enumerative combinatorics
Extremal combinatorics
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Graph theory
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Infinitary combinatorics
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Probabilistic combinatorics
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A
A non-trivial circular argument can often be usefully perturbed to a non-circular one
B
Bijections and counting
I
If a parameter is generating undesirable boundary terms, try averaging over many choices of that parameter
If your problem can be expressed in terms of convolutions and inner products then take the Fourier transform
K
Keep parameters unspecified until it is clear how to optimize them
S
Some useful examples of graphs
T
To compute probabilities of unions and intersections, use the inclusion-exclusion formula
To compute the probability that exactly k of n events occur, use generalized inclusion-exclusion
To increase the occurrence of a property in a set, try randomly refining that set in a way that favors the property
U
Use the compactness and contradiction method to derive finitary quantitative results from infinitary qualitative ones
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Littlewood-Paley heuristic for derivative
Littlewood-Paley heuristic
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Try to prove a stronger result
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Prove a consequence first
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