Related papers: Generating Functions for Multi-j-Symbols
We give some formulas of the James-Hopf maps by using combinatorial methods. An application is to give a product decomposition of the spaces $\Omega\Sigma^2(X)$.
The generating function that records the sizes of directed circuit partitions of a connected 2-in, 2-out digraph D can be determined from the interlacement graph of D with respect to a directed Euler circuit; the same is true of the…
In this work we combine two research threads from Vision/ Graphics and Natural Language Processing to formulate an image generation task conditioned on attributes in a multi-turn setting. By multiturn, we mean the image is generated in a…
A generalization of the Catalan numbers is considered. New results include binomial identities, recursive relations and a close formula for the multivariate generating function. A simple expression for the Catalan determinant is derived.
For a rational function of several variables with nonnegative imaginary part on the upper poly-half-plane, the matrix representations are obtained.
Classical tensors, the familiar mathematical objects denoted by symbols such as $t_{i}$, $t^{ij}$ and $t_{k}^{ij}$, are usually interpreted either as 'coordinatizable objects' with coordinates changing in a specific way under a change of…
We find a set of generators for the automorphism group of a graph product of finitely generated abelian groups entirely from a certain labeled graph. In addition, we find generators for the important subgroup of star-automorphisms defined…
We introduce a novel, systematic method for the complete symbolic reduction of multi-loop Feynman integrals, leveraging the power of generating functions. The differential equations governing these generating functions naturally yield…
We provide a generating function for the (graded) dimensions of M. Kontsevich's graph complexes of ordinary graphs. This generating function can be used to compute the Euler characteristic in each loop order. Furthermore, we show that…
In this paper, we consider situations in which a given logical function is realized by a multithreshold threshold function. In such situations, constant functions can be easily obtained from multithreshold threshold functions, and…
By means of the generating function method, a linear recurrence relation is explicitly resolved. The solution is expressed in terms of the Stirling numbers of both the first and the second kind. Two remarkable pairs of combinatorial…
In this note we define a generalization of Hall-Littlewood symmetric functions using formal group law and give an elementary proof of the generating function formula for the generalized Hall-Littlewood symmetric functions. We also give some…
We consider a number of combinatorial problems in which rational generating functions may be obtained, whose denominators have factors with certain singularities. Specifically, there exist points near which one of the factors is asymptotic…
In this paper, we introduce the generating functions of partition sequences. Partition sequences have a one-to-one correspondence with partitions. Therefore, the generating function has no multiplicity and appears meaningless initially.…
The conceptions of $G$-parking functions and $G$-multiparking functions were introduced in [15] and [12] respectively. In this paper, let $G$ be a connected graph with vertex set $\{1,2,...,n\}$ and $m\in V(G)$. We give the definition of…
The problem of implementing a class of functions with particular conditions by using monotonic multilayer functions is considered. A genetic algorithm is used to create monotonic functions of a certain class, and these are implemented with…
The quantum model of a cluster, consisting of A identical particles, coupled by the internal pair interactions and affected by the external field of a target, is considered. A symbolic-numerical algorithm for generating A-1-dimensional…
Using a simple transfer matrix approach we have derived very long series expansions for the perimeter generating function of three-choice polygons. We find that all the terms in the generating function can be reproduced from a linear…
In this paper, we first introduce certain forms of extended incomplete Pochhammer symbols which are then used to define families of extended incomplete generalized hypergeometric functions. For these functions, we investigate various…
Multisets are an intuitive extension of the traditional concept of sets that allow repetition of elements, with the number of times each element appears being understood as the respective multiplicity. Recent generalizations of multisets to…