The Algebraic Combinatorics Seminar
Scheduled for Fridays at 3:40 PM
Nantel Bergeron and Mike Zabrocki


Schedule

In reverse-chronological order.

Date Speaker Title (click titles for abstract)
1 November, 2013 Trueman
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.
25 October, 2013 Nantel Bergeron How to discover beautiful math in Fibo-Land
Nantel discusses developments in the q-Fibolan numbers, arising from q-deforming the Fibolans and adjusting the combinatorics to match the q-enumeration.
18 October, 2013 Nantel Bergeron Fibolan
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.
20 September, 2013 Nantel Bergeron The Saturation Conjecture and NSym
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.
13 September, 2013 Cesar Ceballos and tom denton Quonting Quores
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.
6 September, 2013 tom denton and Mike Zabrocki Organizational Session
We presented problems that we're interested in working on this year.

Notes.


About the seminar. Every year we pick a new topic to explore. Nantel, Mike and Oded have suggested exploring the 'categorification' of the Heisenberg-like algebra living in End(QSym) or End(NSym).

Year Topic
2012-2013 NSym and the Immaculate Basis
2011-2012 k-Schur functions and affine permutations
2010-2011 Littlewood Richardson rule k-Schur functions.
2009-2010 Idempotents and weakly ordered semigroups. (q,t) Catalan Numbers.
2008-2009 Littlewood-Richardson Rule, Shifted Tableaux and P-Schur functions
2007-2008 Open problems around k-Schur functions and non-commutative symmetric functions
2006-2007 Open problems
2005-2006 Cluster Algebras and Quivers
Spring 2005 Formal languages and analytic classes of functions
Fall 2004 (Quasi-) Symmetric functions in noncommutative variables and applications
Winter 2003 Crystal Bases and Representation Theory, Super-algebras, etc.
Fall 2003 Quasi-Symmetric functions and applications
Fall 2002 Crystal Bases and Representation Theory