Related papers: Calkin-Wilf tree
We study some sequences of polynomials that appear when we consider the successive derivatives of the tree function (or Lambert's W function). We show in particular that they are related with a generalization of Cayley trees, called Greg…
We apply symbolic method to deduce functional equation which generating function of counting sequence of dependency trees must satisfy. Then we use Lagrange inversion theorem to obtain concrete expression of the counting sequence. We apply…
In this paper we present an explicit (rank one) function transform which contains several Jacobi-type function transforms and Hankel-type transforms as degenerate cases. The kernel of the transform, which is given explicitly in terms of…
Motivated by the effective impact of the Pascal functional and the Wronskian matrices, we investigate several identities and differential equation for the Sheffer-Appell polynomial sequence by using matrix algebra. The matrix approach,…
We prove the sufficiency of the Linear Superposition Principle for linear trees, which characterizes the spectra achievable by a real symmetric matrix whose underlying graph is a linear tree. The necessity was previously proven in 2014.…
In this paper we present theorems and applications of Wallis theorem related to trigonometric integrals.
In this work a composition-decomposition technique is presented that correlates tree eigenvectors with certain eigenvectors of an associated so-called skeleton forest. In particular, the matching properties of a skeleton determine the…
The purpose of this note is to study the number of elements in Minkowski bases on algebraic surfaces with rational polyhedral pseudo-effective cone.
Functions of several quaternion variables are investigated and integral representation theorems for them are proved. With the help of them solutions of the $\tilde \partial $-equations are studied. Moreover, quaternion Stein manifolds are…
We obtain new inequalities with alternating signs of H\"{o}lder and Minkowski type.
A tree is scattered if no subdivision of the complete binary tree is a subtree. Building on results of Halin, Polat and Sabidussi, we identify four types of subtrees of a scattered tree and a function of the tree into the integers at least…
A mutation will affect an individual and some or all of its descendants. In this paper, we investigate ordered trees with a distinguished vertex called the mutator. We describe various mutations in ordered trees, and find the generating…
We obtain a closed-form expression for the Wiener index of binomial trees. We outline efficient algorithms for computing the Wiener indices of Fibonacci and binary Fibonacci trees.
In this paper, we gave some properties of binomial coefficient.
This note gives a short proof on characterizations of a forest to be equitably k-colorable.
In this work we prove a Brunn-Minkowski-type inequality in the context of symplectic geometry and discuss some of its applications.
We prove pointwise relations between some multiparameter square functions on $\bold R^n$.
This talk is a report on joint work with A. Vaintrob [arXiv:math.CO/0109104 and math.GT/0111102]. It is organised as follows. We begin by recalling how the classical Matrix-Tree Theorem relates two different expressions for the lowest…
We introduce a theory of multigraded Cayley-Chow forms associated to subvarieties of products of projective spaces. Two new phenomena arise: first, the construction turns out to require certain inequalities on the dimensions of projections;…
Consider $G=SL_2(\mathbb{Z})/\{\pm I\}$ acting on the complex upper half plane $H$ by $h_M(z)=\frac{az+b}{cz+d},$ for $M \in G$. Let $D=\{z \in H: |z|\geq 1, |\Re(z)|\leq 1/2\}$. We consider the set $\mathcal{E} \subset G$ with the $9$…