Results 181 to 190 of about 62,131 (208)

Monomials, Polynomials and Binomials

2013
In this chapter we will be primarily interested in the study of monomials and polynomials within the framework of quaternion analysis. Monomials and their applications to combinatorics and number theory have become increasingly important for the study of a large number of problems that arise in many different contexts, both from a theoretical and a ...
João Pedro Morais, Svetlin Georgiev, Wolfgang Sprößig   +2 more
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Diophantine equations with truncated binomial polynomials

Indagationes Mathematicae, 2016
The authors consider the Diophantine equation \(P_{n,k}(x)=P_{m,\ell}(y)\) in integers \(x,y\), where, for positive integers \(k\leq n\), \(P_{n,k}(x)=\sum_{j=0}^k {n\choose j}x^j\) is a truncated binomial expression of \((1+x)^n\). Under certain irreducibility assumptions, they show that the equation admits only finitely many solutions.
Dubickas, Artūras, Kreso, Dijana
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Polynomials of Binomial Type and Renewal Sequences

Studies in Applied Mathematics, 1987
We study polynomials of binomial type that have an exponential generating function of the form { 1 − f(u)−x}. They have a close connection with renewal sequences. The asymptotic behavior as n − ∞ is studied.
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Polynomial expressions for non-binomial structures

Theoretical Computer Science, 2019
Let \(R=K[x_1,\ldots ,x_n]\) be a polynomial ring over a field \(K\) and \(f,f_1,\ldots ,f_k\in R\). Let us fix a term ordering on \(R\). The classical division algorithm claims that one is able to write \(f\) as an expression like \(g_1f_1+\cdots +g_kf_k+h\) where either \(h=0\) or no term in \(h\) is divisible by the leading terms of the \(f_i\)'s ...
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Binomial formula for Macdonald polynomials and applications

Mathematical Research Letters, 1997
The author gives the non-evident and the very non-trivial generalization of the Macdonald polynomials. He defines the ``interpolation Macdonald polynomial'' \(P^*(x_1,\dots, x_n;q,t)\) (\(q\) and \(t\) are two parameters) by the following conditions: (1) \(P^*\) is symmetric in variables \(x_i t_i^{-1}\), (2) \(\deg P_\mu^*=| \mu|\) for any partition \(
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BINOMIAL IDENTITIES INVOLVING THE GENERALIZED FIBONACCI TYPE POLYNOMIALS

2011
We present some binomial identities for sums of the bivariate Fibonacci polynomials and for weighted sums of the usual Fibonacci polynomials with indices in arithmetic progression.
Kilic, Emrah, Irmak, Nurettin
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3. Binomial polynomial sequences

2019
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Binomial Sequences of Polynomials

2000
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Polynomials with the Binomial Property

The American Mathematical Monthly, 1957
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The Galois Group of a Binomial Polynomial

Proceedings of the London Mathematical Society, 1953
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