K terms recurrence relations and polynomial variance functions of the Kth degree

Recurrence Relations and Generating Functions

a synchronic and diachronic approach to the change route of address terms in the two recent centuries of persian language

terms of address as an important linguistics items provide valuable information about the interlocutors, their relationship and their circumstances. this study was done to investigate the change route of persian address terms in the two recent centuries including three historical periods of qajar, pahlavi and after the islamic revolution. data were extracted from a corpus consisting 24 novels w...

Recurrence Relations and Splitting Formulas for the Domination Polynomial

The domination polynomial D(G, x) of a graph G is the generating function of its dominating sets. We prove that D(G, x) satisfies a wide range of reduction formulas. We show linear recurrence relations for D(G, x) for arbitrary graphs and for various special cases. We give splitting formulas for D(G, x) based on articulation vertices, and more generally, on splitting sets of vertices.

Boolean Functions Of Low Polynomial Degree

Boolean functions of high deterministic query complexity and low degree of representing polynomial have different applications in theoretical computer science, yet not many are known with such properties. We analyze some previously known and construct several new functions with such properties.

Linear Recurrence Relations for Sums of Products of Two Terms

For a sum of the form ∑ k F (n, k)G(n, k), we set up two systems of equations involving shifts of F (n, k) and G(n, k). Then we solve the systems by utilizing the recursion of F (n, k) and the method of undetermined coefficients. From the solutions, we derive linear recurrence relations for the sum. With this method, we prove many identities involving Bernoulli numbers and Stirling numbers.