arXiv subjects
Publications and source records attributed to Mong Lung Lang.
By investigating a recurrence relation about functions, we first give alternative proofs of various identities on Fibonacci numbers and Lucas numbers, and then, make certain well known identities visible via certain trivalent graph associated to the recurrence relation.
We determine the ranks and normal ranks of the Sylow 2-subgroups of the classical groups of odd characteristic.
We determine the ranks of the Sylow 2-subgroups of the classical simple groups of odd characteristic.
We determine the normalisers of congruence subgroups of $G_5$.
Let $R$ be an indecomposable root system. It is well known that any root is part of a basis $B$ of $R$. But when can you extend a set of two or more roots to a basis $B$ of $R$? A $π$-system is a linearly independent set of roots, $C$, such that if $α$ and $β$ are in $C$, then $α- β$ is not a root. We will use results of Dynkin and Bourbaki to show that with two exceptions, $A_3 \subset B_n$ and $A_7 \subset E_8$, an indecomposable $π$-system whose Dynkin diagram is a subdiagram of the Dynkin diagram of $R$ can always be extended to a basis of $R$.
We give a simple and independent proof of the result of Jack Button and Paul Schmutz that the Markoff conjecture on the uniqueness of the Markoff triples (a,b,c), where a, b, and c are in increasing order, holds whenever $c$ is a prime power.
Let $ \Bbb V = \coprod_{h = 0}^{\infty} \Bbb V_h$ be the graded monster module of the monster simple group $\Bbb M$ and let $χ_k$ be an irreducible representation of $\Bbb M$. The generating function of $c_{hk}$ (the multiplicity of $χ_k$ in $\Bbb V_h$) is determined. Furthermore, the invariance group of the modular function associated with the generating function is also determined in this paper.
We investigate the relation between the generating functions of the highest weight vectors of the Monster module and the McKay-Thompson series.