The incompressibility method is an elementary yet powerful proof technique. It has been used successfully in many areas [8]. To further demonstrate its power and elegance we exhibit new simple proofs using the incompressibility method.

The incompressibility method is an elementary yet powerful proof technique. It has been used successfully in many areas [11]. To further demonstrate its power and elegance we exhibit new simple proofs using the incompressibility method.

Heilbronn’s triangle problem asks for the least ∆ such that n points lying in the unit disc necessarily contain a triangle of area at most ∆. Heilbronn initially conjectured ∆ = O(1/n). As a result of concerted mathematical effort it is currently known that there are positive constants c and C such that c logn/n ≤ ∆ ≤ C/n for every constant ǫ > 0. We resolve Heilbronn’s problem in the expected ...

We show how incompressibility, a well-described property of some prosodic timing effects, can be accounted for in an optimization-based model of speech timing. Preliminary results of a corpus study are presented, replicating and generalizing previous findings on incompressibility as a function of increasing speaking rate. We then introduce the architecture of our model and present results of si...