ICE-TCS seminar: Omer Egecioglu
Combinatorics of an Euler-like product with Fibonacci exponents
ICE-TCS seminar #326
Date and time: Tuesday, 15 January 2019, 12:10-13:00
Location: Room M1.20 (note the new room for the spring 2019 semester)
Speaker: Omer Egecioglu (University of California at Santa Barbara, visiting RU)
WWW: http://www.cs.ucsb.edu/~omer/
Title: Combinatorics of an Euler-like product with Fibonacci exponents
Abstract: Once we interpret the famous product (1-y) (1-y^2) (1-y^3)(1-y^4)(1-y^5)..... of Euler in the setting of integer partitions, the nature of the resulting series boils down to relatively simple pairing of partitions in a sign-reversing manner, showing that the expansion has coefficients from { -1, 0, 1}. Are there other interesting sequences of exponents for which the coefficients of the expansion are from { -1, 0, 1}?
One such sequence is the Fibonacci numbers. The analysis of the expansion in this case involves
some interesting combinatorial tools including automata theory, modular arithmetic, finite monoids,
partitions and Markov chains.
This is work in progress.
