Hamming polynomials and their partial derivatives
نویسندگان
چکیده
منابع مشابه
Hamming polynomials and their partial derivatives
Hamming graphs are Cartesian products of complete graphs and partial Hamming graphs are their isometric subgraphs. The Hamming polynomial h(G) of a graph G is introduced as the Hamming subgraphs counting polynomial. Kk-derivates ∂kG (k ≥ 2) of a partial Hamming graph are also introduced. It is proved that for a partial Hamming graph G, ∂h(G) ∂xk = h(∂kG). A couple of combinatorial identities in...
متن کاملB - 433 Efficient Evaluation of Polynomials and Their Partial Derivatives in Homotopy Continuation Methods
The aim of this paper is to study how efficiently we evaluate a system of multivariate polynomials and their partial derivatives in homotopy continuation methods. Our major tool is an extension of the Horner scheme, which is popular in evaluating a univariate polynomial, to a multivariate polynomial. But the extension is not unique, and there are many Horner factorizations of a given multivaria...
متن کاملEfficient Evaluation of Polynomials and Their Partial Derivatives in Homotopy Continuation Methods
The aim of this paper is to study how efficiently we evaluate a system of multivariate polynomials and their partial derivatives in homotopy continuation methods. Our major tool is an extension of the Horner scheme, which is popular in evaluating a univariate polynomial, to a multivariate polynomial. But the extension is not unique, and there are many Horner factorizations of a given multivaria...
متن کاملOn the L2 Inequalities Involving Trigonometric Polynomials and Their Derivatives
In this note we study the upper bound of the integral f {tW(x))2w(x)dx Jo where t(x) is a trigonometric polynomial with real coefficients such that \\t\\ao < 1 and w(x) is a nonnegative function defined on [0, n]. When w{x) = sin; x , where j is a positive integer, we obtain the exact upper bound for the above integral.
متن کاملA Combinatorial Interpretation of Lommel Polynomials and Their Derivatives
In this paper we present interpretations of Lommel polynomials and their derivatives. A combinatorial interpretation uses matchings in graphs. This gives an interpretation for the derivatives as well. Then Lommel polynomials are considered from the point of view of operator calculus. A step-3 nilpotent Lie algebra and finite-difference operators arise in the analysis.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2007
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2006.03.001