Some Catalan Musings

Monday, November 10, 2014 - 9:00am - 9:50am
Keller 3-180
Richard Stanley (Massachusetts Institute of Technology)
The sequence 1, 1, 2, 5, 14, 42, ... of Catalan numbers is probably
the most ubiquitous and most interesting sequence in
combinatorics. For instance, the Online Encyclopedia of Integer
Sequences says that the Catlan number entry A000108 is probably the
longest entry in the OEIS, and rightly so. I have recently completed
a monograph on Catalan numbers, to be published by Cambridge
University Press. I will give a sample of results from this monograph,
including selections from the history of Catalan numbers, their
transparent combinatorial interpretations, more subtle combinatorial
interpretations, algebraic interpretations, and analytic and
number-theoretic properties.
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