Basketball fans are always amazed when a shooter goes on a seemingly unbelievable hot steak. But is the “hot hand” really an anomaly, or is the sequence of makes and misses to be expected by simple chance? This study uses free throw statistics to analyze the “hot hand” with several different... more
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We present several generating functions for sequences involving the central binomial coefficients and the harmonic numbers. In particular, we obtain the generating functions for the sequences C(2n,n)*H_n, C(2n,n)*(1/n)*H_n, C(2n,n)(1/(n+1))*H_n and C(2n,n)*n^m. The technique is based on a... more
In the NFL the best and worst team regular season records in modern times were as follows: In 2007 the New England Patriots went 16 – 0, and in 2008 the Detroit Lions went 0 – 16. In the NBA the best and worst team regular season records in modern times were as follows: In 1995-96 the... more
This is a short introduction to the theory of Stirling numbers of the second kind S(m, k) from the point of view of analysis. It is written as an historical survey centered on the representation of these numbers by a certain binomial transform formula. We tell the story of their birth in the... more
A general probabilistic argument may be used to prove the existence of the so-called "k-paradoxical" tournaments. We will explore a few arithmetical ways of explicitly constructing examples of such tournaments. The full conference program can be found... more
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