2008 REU on Rational Generating Functions for Permutation Patterns

Participants:

Generating functions encode the solution to counting problems in enumerative combinatorics. Among the nicest generating functions are those which can be expressed as a ratio of two polynomials. The coefficients of these "rational generating functions" satisfy a linear constant coefficient recurrence. Permutation patterns are a source of many diverse generating functions in modern enumerative combinatorics. However, it remains a difficult problem to classify which permutation pattern classes lead to rational generating functions. In this REU, we seek out new examples of rational permutation pattern classes. One aspect of the project involves collecting sequence data by writing computer programs.

See the REU notes for more details.

Links:
Sloane's online encyclopedia of integer sequences
Tenner's database of permutation pattern avoidance
MathSciNet to search for articles