Trueman discusses work relating Fibonacci and Lucas numbers to the homogeneous and power symmetric functions. The hook-Schur functions (another free algebraic basis of Sym) also made an appearance. The hope is to relate these objects to the ongoing study of the q-Fibolan numbers.
Nantel Bergeron presents on the 'Fibolan' numbers recently discovered by Sagan and Savage. These are a replacement of the usual integers with Fibonacci numbers in the formula for binomial coefficients. Sagan and Savage have developed a combinatorial object that these numbers count.
Nantel presented an approach to the saturation conjecture (which is no longer a conjecture in Sym) for NSym, using a polytope realized from the immaculate basis. He also talked about the dual quasi-Schur functions, and possibilities for creating a polytope for the relevant composition tabeleaux, which could then be used to attack the saturaation conjecture for that basis.
We present the lattice path model for computing statistics on simultaneous core partitions. The lattice path model allows us to quickly compute the skew length statistic, conjectured to be the q-statistic for simultaneous (a,b)-cores when a and b are relatively prime. We demonstrate that the skew length is symmetric in a and b.