In a tradition that is in its 20th year, Donald Knuth presented his 2014 Christmas Tree lecture at Stanford University earlier this month. His topic, as always, is related to something new about trees he learned during the year - in this instance (3/2)-ary Trees.

Trees are important at this time of the year, at least in the parts of the world that celebrate Xmas. However for programmers trees are always important. They are the fundamental advanced data structure that while seeming simple have lots of surprising and remarkable properties.

Donald Knuth should be known to you but just in case - he invented the TeX computer typesetting system, is the author of the monumental work The Art of Computer Programming and many algorithms. He also has a strange sense of humour so look out for it when you watch the video.  

The notes to the lecture tell you pretty much what it is all about:

In previous lectures Professor Knuth has discussed binary trees, ternary trees, quaternary trees, etc., which are enumerated by the coefficients of important functions called generalized binomial series of order 2, 3, 4, etc. What happens when we consider generalized binomial series of order 3/2, or of other fractional orders? The answer is pretty amazing.

The lecture proper starts about 4 minutes in - and be warned it is over an hour long and it is difficult to follow if you don't know finite math as explained in Knuth's book Concrete Math. If you get a bit discouraged by the math at the start then try to keep going because it gets increasingly interesting and more oriented to computer science as it goes on: 

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