In this paper, we define bi-periodic (p,q)-Fibonacci and (p,q)-Lucas sequences, which generalize Fibonacci type, Lucas type using recurrence relations of sequences. Generating functions Binet formulas that allow us to calculate the nth terms these sequences are given convergence properties their consecutive examined. Also, prove some fundamental identities conform well-known

In this paper, we introduce a tiling approach to (p,q)-Fibonacci and (p,q)-Lucas numbers that generalize of the well-known Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal ve Jacobsthal-Lucas numbers. We show nth number is interpreted as ways tile 1×n board with cells labeled 1,2,...,n using colored 1×1 squares 1×2 dominoes, where there are p kind colors for q dominoes. Then circular also present...

Let p > q and let G be the group U(p, q) or Spin0(p, q). Let P = LN be the maximal parabolic subgroup of G with Levi subgroup L ∼=M × U where (M,U) = { (GLq(C),U(p− q)) if G = U(p, q) (GLq (R),Spin(p− q)) if G = Spin0(p, q). Let χ be a 1 dimensional character of M and τ an irreducible representation of U with highest weight μ. Let πχ,μ be the representation of P which is trivial on N and πχ,μ|L...