Section: New Results

On sequences associated to the invariant theory of rank two simple Lie algebras

In [14], Alin Bostan together with Jordan Tirrell (Washington College, USA) Philadelphia, USA), Bruce W. Westbury (Unversity of Texas at Dallas, USA) and Yi Zhang (Xi'an Jiaotong-Liverpool University, Suzhou, China) studied two families of sequences, listed in the On-Line Encyclopedia of Integer Sequences (OEIS), which are associated to invariant theory of Lie algebras. For the first family, they proved combinatorially that the sequences A059710 and A108307 are related by a binomial transform. Based on this, they presented two independent proofs of a recurrence equation for A059710, which was conjectured by Mihailovs. Besides, they also gave a direct proof of Mihailovs’ conjecture by the method of algebraic residues. As a consequence, closed formulae for the generating function of sequence A059710 were obtained in terms of classical Gaussian hypergeometric functions.