• Corpus ID: 208268117

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

@article{Bostan2019OnSA,
  title={On sequences associated to the invariant theory of rank two simple Lie algebras},
  author={Alin Bostan and Jordan Olliver Tirrell and Bruce W. Westbury and Yi Zhang},
  journal={ArXiv},
  year={2019},
  volume={abs/1911.10288}
}
We study 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, we prove combinatorially that the sequences A059710 and A108307 are related by a binomial transform. Based on this, we present two independent proofs of a recurrence equation for A059710, which was conjectured by Mihailovs. Besides, we also give a direct proof of Mihailovs' conjecture by the method of algebraic… 
2 Citations

Figures from this paper

A criterion for asymptotic sharpness in the enumeration of simply generated trees
We study the identity $y(x)=xA(y(x))$, from the theory of rooted trees, for appropriate generating functions $y(x)$ and $A(x)$ with non-negative integer coefficients. A problem that has been studied

References

SHOWING 1-10 OF 20 REFERENCES
Spiders for rank 2 Lie algebras
A spider is an axiomatization of the representation theory of a group, quantum group, Lie algebra, or other group or group-like object. It is also known as a spherical category, or a strict, monoidal
Enumeration of non-positive planar trivalent graphs
In this paper we construct inverse bijections between two sequences of finite sets. One sequence is defined by planar diagrams and the other by lattice walks. In [13] it is shown that the number of
Advanced applications of the holonomic systems approach
TLDR
This thesis contributed to translating Takayama's algorithm into a new context, in order to apply it to an until then open problem, the proof of Ira Gessel's lattice path conjecture, and to make the underlying computations feasible the authors employed a new approach for finding creative telescoping operators.
ON PARTITIONS AVOIDING 3-CROSSINGS
A partition on (n) has a crossing if there exists i1 < i2 < j1 < j2 such that i1 and j1 are in the same block, i2 and j2 are in the same block, but i1 and i2 are not in the same block. Recently, Chen
Restricted inversion sequences and enhanced 3-noncrossing partitions
Crossings and nestings of matchings and partitions
We present results on the enumeration of crossings and nestings for matchings and set partitions. Using a bijection between partitions and vacillating tableaux, we show that if we fix the sets of
Creative telescoping for rational functions using the griffiths: dwork method
TLDR
This work describes a precise and elementary algorithmic version of the Griffiths-Dwork method for the creative telescoping of rational functions that leads to bounds on the order and degree of the coefficients of the differential equation, and to the first complexity result which is single exponential in the number of variables.
...
1
2
...