Dear all,
The next talk is by Bishal Deb of University College, London. Here is the announcement.
Title: The "quadratic family" of continued fractions and combinatorial sequences
Speaker: Bishal Deb (University College, London)
When: May 11, 2023, 4:00 PM- 5:00 PM IST (11:30 AM BST)
Where: Zoom:
Abstract
We will begin this talk by introducing some combinatorial sequences whose Stieltjes-type continued fraction coefficients increase linearly. We briefly mention the work of Sokal and Zeng where they systematically studied multivariate generalisations of these continued fractions for factorials, Bell numbers and double factorials.
Next, we will define the Genocchi and median Genocchi numbers and introduce D-permutations, a class of permutations which enumerate these numbers. We mention some multivariate continued fractions counting various statistics on D-permutations.
Finally, we move to the secant numbers and introduce cycle-alternating permutations; these are another class of permutations which enumerate the secant numbers. We mention some multivariate continued fractions counting various statistics on cycle-alternating permutations. We then describe the entries in the Jacobi-Rogers matrix of our continued fraction using alternating Laguerre digraphs, which are a class of directed graphs. If time permits, we will briefly state some remarks on the Jacobian elliptic functions.
This talk will be based on joint work with Alan Sokal.
Next, we will define the Genocchi and median Genocchi numbers and introduce D-permutations, a class of permutations which enumerate these numbers. We mention some multivariate continued fractions counting various statistics on D-permutations.
Finally, we move to the secant numbers and introduce cycle-alternating permutations; these are another class of permutations which enumerate the secant numbers. We mention some multivariate continued fractions counting various statistics on cycle-alternating permutations. We then describe the entries in the Jacobi-Rogers matrix of our continued fraction using alternating Laguerre digraphs, which are a class of directed graphs. If time permits, we will briefly state some remarks on the Jacobian elliptic functions.
This talk will be based on joint work with Alan Sokal.
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