相关论文: A new formula for the generating function of the n…

The methods of classical invariant theory are used to construct generic polynomials for groups $S_5$ and $A_5$, along with explicit reductions to specializations of the generic polynomials defining any desired field extension with those…

We introduce graph normalizing flows: a new, reversible graph neural network model for prediction and generation. On supervised tasks, graph normalizing flows perform similarly to message passing neural networks, but at a significantly…

In this paper we establish a bridge between Topological Data Analysis and Geometric Deep Learning, adapting the topological theory of group equivariant non-expansive operators (GENEOs) to act on the space of all graphs weighted on vertices…

In this paper we relate a fundamental parameter of a random graph, its degree sequence, to a simple model of nearly independent binomial random variables. This confirms a conjecture made in 1997. As a result, many interesting functions of…

From any given sequence of finite or infinite graphs, a nonstandard graph is constructed. The procedure is similar to an ultrapower construction of an internal set from a sequence of subsets of the real line, but now the individual entities…

This article present a new, direct and simple formula for constructing Mignotte sequences.

We introduce a new set of prime numbers functions including an exact Generating Function and a Discriminating Function of Prime Numbers neither based on prime number tables nor on algorithms. Instead these functions are defined in terms of…

Let $G=(V,E)$ be a loopless graph and $\mathcal{T}(G)$ be the set of all spanning trees of $G$. Let $L(G)$ be the line graph of the graph $G$ and $t(L(G))$ be the number of spanning trees of $L(G)$. Then, by using techniques from electrical…

We describe a simple algorithm based on a Markov chain process to generate simply connected acyclic directed graphs over a fixed set of vertices. This algorithm is an extension of a previous one, designed to generate acyclic digraphs, non…

With an arbitrary finite graph having a special form of 2-intervals (a diamond-shaped graph) we associate a subgroup of a symmetric group and a representation of this subgroup; state a series of problems on such groups and their…

An algorithm is given for computing explicit formulas for the generators of relations among the invariant rational functions for vector-valued bilinear forms. These formulas have applications in the geometry of Riemannian submanifolds and…

We present new combinatorial insights into the calculation of (Castelnuovo-Mumford) regularity of graphs.

We present and investigate an extension of the classical random graph to a general class of inhomogeneous random graph models, where vertices come in different types, and the probability of realizing an edge depends on the types of its…

We construct new integral representations for transformations of the ordinary generating function for a sequence, $\langle f_n \rangle$, into the form of a generating function that enumerates the corresponding "square series" generating…

An explicit form of the generators of quantum and ordinary semisimple algebras for an arbitrary finite-dimensional representation is found. The generators corresponding to the simple roots are obtained in terms of a solution of a system of…

For a given spectral curve, we construct a family of symplectic dual spectral curves for which we prove an explicit formula expressing the $n$-point functions produced by the topological recursion on these curves via the $n$-point functions…

Given a finite group $G$, the invariably generating graph of $G$ is defined as the undirected graph in which the vertices are the nontrivial conjugacy classes of $G$, and two classes are adjacent if and only if they invariably generate $G$.…

Previous work on symmetric group equivariant neural networks generally only considered the case where the group acts by permuting the elements of a single vector. In this paper we derive formulae for general permutation equivariant layers,…

In this paper, we introduce a novel approach for generating random elements of a finite group given a set of generators of that. Our method draws upon combinatorial group theory and automata theory to achieve this objective. Furthermore, we…

The problem of a restricted random walk on graphs which keeps track of the number of immediate reversal steps is considered by using a transfer matrix formulation. A closed-form expression is obtained for the generating function of the…