ICE-TCS seminar: Omer Egecioglu

Combinatorics of an Euler-like product with Fibonacci exponents

  • 15.1.2019, 12:10 - 13:00

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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.