October 11, 2014 – Dr. Walter Stromquist – “Permutation Patterns”

Please join us for a fun look at permutation patterns.  We will count some special classes of permutations.  For example, there are “132-avoiding” permutations, which are those (like 546231) that never have three entries in order smallest-largest-middle.  Among the n! permutations of size n, how many are 132-avoiding?  And how many are 123-avoiding?  That question is just the beginning.  Next, we can count the number of permutations with 3 “descents”—downsteps between consecutive entries—again, like 546231—or the number of permutations with 3 “excedences”—cases of pi(i)>i—again, like 546231.  There is a connection, which is another beginning.  All this can be unified, and we’ll try to do that using “triangular functions.”