Title: Fomin Growth Diagrams or How I Learned to Stop Worrying and Love Young Tableaux
Speaker: Keith Frankston, Rutgers University
Date: Wednesday, March 22, 2017 12:10pm
Location: Graduate Student Lounge, 7th Floor, Hill Center, Rutgers University, Busch Campus, Piscataway, NJ
This talk will be an introduction to the combinatorial tool I call Fomin Growth Diagrams. These diagrams are natural number arrays augmented with partitions. The specific partitions that appear are governed by a ruleset which grows them from an initial arrangement to an assignment over the entire array. In particular, we will describe the ruleset controlling the growth and show it produces a bijective relationship between initial conditions and last stage of growth. Once we have proven that the underlying ruleset produces a bijection, by restricting the initial conditions of the underlying array, we will derive a number of non-trivial combinatorial bijections with almost no work (in particular, RSK and the Schur identity). In fact, for RSK, we will get as a corollary a result that would otherwise require significant work in and of itself. While I won't go into further applications, I hope to convince everyone that this is a powerful tool when dealing with Young Tableaux (and it even can be used in some seemingly unrelated applications). In addition, this is far from the only ruleset you can choose to produce such structures. I will start the talk with a brief introduction to partitions, tableaux and Schur functions (though it certainly won't hurt if you've seen any or all of these concepts before).