TL;DR: In this article, a new technique is evolved to give operator representation of polynomials in the MOS Subject Classification (MOS) subject classification (2000): Primary 47F05, Secondary 33C4.
Abstract: A new technique is evolved to give operator representation of certain polynomials. AMS (MOS) Subject Classification (2000): Primary 47F05, Secondary 33C4.
TL;DR: In this paper, Moshe's algorithm for computing the Lyapunov exponent for 2x2 random matrix products is reviewed and further examples with more terms and higher powers of x are analyzed.
Abstract: The nth row of Pascal's trinomial triangle gives coefficients of (1+x+x^2)^n. Let g(n) denote the number of such coefficients that are odd. We review Moshe's algorithm for evaluating asymptotics of g(n) -- this involves computing the Lyapunov exponent for certain 2x2 random matrix products -- and then analyze further examples with more terms and higher powers of x.
TL;DR: In this paper, the Trinomial Triangle has been studied in the context of mathematics and science, and it is shown that it is possible to construct a trinomial triangle from the triangulation.
Abstract: (1999). The Trinomial Triangle. The College Mathematics Journal: Vol. 30, No. 2, pp. 141-142.
TL;DR: In this paper, several congruences for trinomial coefficients were proved for the case of trinomials, including the following congruence for the triangulation:
Abstract: We prove several congruences for trinomial coefficients.
TL;DR: In this article, the central trinomial coefficients and the Motzkin numbers were proved for the first time, and two new formulas for the central Trinomial coefficient were proposed.
Abstract: We prove two new formulas for the central trinomial coefficients and the Motzkin numbers.