Somos sequences and bilinear combinatoricsJames ProppUniversity of Wisconsin and MIT
October 18,

ABSTRACT


Linear recurrences (and, with them, ordinary generating functions) are ubiquitous in combinatorics, as part of a broad general framework that is wellstudied and wellunderstood; in contrast, bilinear recurrences such as In this talk I will describe some types of combinatorial objects whose properties make them wellsuited to a (nascent) general theory of bilinear recurrence relations. In some interesting cases (e.g., the Somos4 recurrence given above), algebra is one step ahead of combinatorics, and we are temporarily in the unusual position of being able to enumerate combinatorial objects for which we lack a combinatorial description! I will attempt to convince members of the audience that some basic problems connected with bilinear recurrence relations are compelling and accessible. If I succeed at this, I plan to organize a working group that will jointly explore these problems over the next several months. (Most of the lecture should be accessible to advanced undergraduates.) 
Combinatorics Seminar, Mathematics Department, MIT, sara(atsign)math.mit.edu 

