Abstract We develop a representation theory approach to the study of generalized hypergeometric functions Gelfand, Kapranov and Zelevisnky (GKZ). show that GKZ may be identified with matrix elements non-reductive Lie algebras $${\mathfrak L}_N$$ L N oscillator type. The...

In this letter, the random matrix theory representation of a bond-percolation model on square lattice is presented. The behavior can be determined only by its two largest eigenvalues. second eigenvalue sits exactly edge semicircle part eigenvalue’s distribution and position function p, other hand first disjointed from eigenvalues Gaussian. Also responsible for scaling properties near criticalit...

In this paper we give a new generalization of the Pell numbers in matrix representation. Also we extend the matrix representation and we show that the sums of the generalized order-k Pell numbers could be derived directly using this representation. Further we present some identities, the generalized Binet formula and combinatorial representation of the generalized order-k Pell numbers.