From Catalan numbers to integrable dynamics: continued fractions and Hankel determinants for q-numbers

Abstract: The classical Catalan and Motzkin numbers have remarkable continued fraction expansions, the corresponding sequences of Hankel determinants consist of -1, 0 and 1 only. We find an infinite family of power series corresponding to q-deformed real numbers that have very similar properties. Moreover, their sequences of Hankel determinants turn out to satisfy Somos and Gale-Robinson recurrences. (Partially based on a joint work with Emmanuel Pedon.)

dynamical systemsnumber theory

Audience: researchers in the topic

( paper | slides )

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One World Numeration seminar

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