Euler’s ship on the pentagonal sea

  • Johannes W. Meijer
  • Manuel Nepveu


Probability is a rich part of applied mathematics. First we have a look at the
unique encounter of two 23 year old chess players on their birthday which
leads to an interesting set of questions. Next some chess tournaments lead us
to partition numbers, multinomial coefficients and Bell numbers. After that we
arrive at the Pentagonal Sea where the beautiful structure of Euler’s ship leads
to a new look at the recurrence relation of the partition function and the
pentagonal number theorem. Aboard Euler’s ship we find the Lazy Caterer’s
and the Connell sequences. At the end we look at the probability that the
above mentioned chess confrontation will ever happen again and tell you how
to decide whether to accept or reject a wager.

Artículos de Investigación