11 citations · 31 across the 8 of their papers we have counts for
9 papers
An Algorithmic Approach to Emergence
Charles Alexandre Bédard, Geoffroy Bergeron
We suggest a quantitative and objective notion of emergence. Our proposal uses algorithmic information theory as a basis for an objective framework in which a bit string encodes ob…
Orthogonal polynomials and the deformed Jordan plane
André Beaudoin, Geoffroy Bergeron, Antoine Brillant +3
We consider the unital associative algebra with two generators , obeying the defining relation .…
The rational Sklyanin algebra and the Wilson and para-Racah polynomials
Geoffroy Bergeron, Julien Gaboriaud, Luc Vinet +1
The relation between Wilson and para-Racah polynomials and representations of the degenerate rational Sklyanin algebra is established. Second order Heun operators on quadratic grid…
Sklyanin-like algebras for (-)linear grids and (-)para-Krawtchouk polynomials
Geoffroy Bergeron, Julien Gaboriaud, Luc Vinet +1
S-Heun operators on linear and -linear grids are introduced. These operators are special cases of Heun operators and are related to Sklyanin-like algebras. The Continuous Hahn a…
The Heun-Racah and Heun-Bannai-Ito algebras
Geoffroy Bergeron, Nicolas Crampé, Satoshi Tsujimoto +2
This paper introduces and studies the Heun-Racah and Heun-Bannai-Ito algebras abstractly and establishes the relation between these new algebraic structures and generalized Heun-ty…
Signal processing, orthogonal polynomials, and Heun equations
Geoffroy Bergeron, Luc Vinet, Alexei Zhedanov
A survey of recents advances in the theory of Heun operators is offered. Some of the topics covered include: quadratic algebras and orthogonal polynomials, differential and differe…
corepresentations and bivariate -Krawtchouk polynomials
Geoffroy Bergeron, Erik Koelink, Luc Vinet
The matrix elements of unitary corepresentations, which are analogues of the symmetric powers of the natural repesentation, are shown to be the bivariate -Krawtchouk o…
Generating functions for the Bannai-Ito polynomials
Geoffroy Bergeron, Luc Vinet, Satoshi Tsujimoto
The generating function of the Bannai-Ito polynomials is derived using the fact that these polynomials are known to be essentially the Racah or coefficients of the $\mathfrak{…
Generating functions for the osp(1|2) Clebsch-Gordan coefficients
Geoffroy Bergeron, Luc Vinet
Generating functions for Clebsch-Gordan coefficients of osp(1|2) are derived. These coefficients are expressed as q goes to - 1 limits of the dual q-Hahn polynomials. The generatin…