Related papers: On the asymptotics of higher-dimensional partition…
Understanding distance metrics in high-dimensional spaces is crucial for various fields such as data analysis, machine learning, and optimization. The Manhattan distance, a fundamental metric in multi-dimensional settings, measures the…
We study the asymptotic behavior of double and four circulant codes, which are quasi-cyclic codes of index two and four respectively. Exact enumeration results are derived for these families of codes with the prescribed hull dimension.…
Let N_{a,b}(x) count the number of primes p<=x with p dividing a^k+b^k for some k>=1. It is known that asymptotically N_{a,b}(x) grows like c(a,b)x/log x for some rational number c(a,b) that depends in a rather intricate way on a and b. A…
In light of Kim's conjecture on regular polytopes of dimension four, which is a generalization of Waring's problem, we establish asymptotic formulas for representing any sufficiently large integer as a sum of numbers in the form of those…
Motivated by a question of V. Bergelson and F. K. Richter (2017), we obtain asymptotic formulas for the number of relatively prime tuples composed of positive integers $n\le N$ and integer parts of polynomials evaluated at $n$. The error…
Let A be a set of positive integers with gcd(A) = 1, and let p_A(n) be the partition function of A. Let c = \pi \sqrt(2/3). Let \alpha > 0. It is proved that log p_A(n) ~ c\sqrt(\alpha n) if and only if the set A has asymptotic density…
In this paper we strongly improve asymptotics for $s_1(n)$ (respectively $s_2(n)$) which sums reciprocals (respectively squares of reciprocals) of parts throughout all the partitions of $n$ into distinct parts. The methods required are much…
Three-dimensional discrete numerical simulation is used to investigate the properties of close-packed frictionless granular assemblies as a function of particle polydispersity and shape. Unlike some experimental results, simulations show…
Consider an arbitrary extension of a free $\mathbb Z^d$-action on the Cantor set. It is shown that it has dynamical asymptotic dimension at most $3^d - 1$.
We develop a theory for the representation of opaque solids as volumes. Starting from a stochastic representation of opaque solids as random indicator functions, we prove the conditions under which such solids can be modeled using…
We study the questions of determining the asymptotics of the probabilistic characteristics of additive arithmetic functions in the paper, regardless of whether they have a limit distribution or not. Several assertions are proved about the…
In this article, we introduce the notion of almost consecutive partitions. A partition is almost consecutive if every term is consecutive, with the possible exception of the smallest one. We find formulas relating to the smallest parts of…
We give a complete rigorous proof of the full asymptotic expansion of the partition function of the dimer model on a square lattice on a torus for general weights $z_h, z_v$ of the dimer model and arbitrary dimensions of the lattice $m, n$.…
It is demonstrated that the complex scaling method can be used in practical calculations to localize three-body resonances. Our model example emphasizes the fact that in three-body systems several essentially different asymptotic behaviors…
The counting of the dimension of the space of $U(N) \times U(N) \times U(N)$ polynomial invariants of a complex $3$-index tensor as a function of degree $n$ is known in terms of a sum of squares of Kronecker coefficients. For $n \le N$, the…
Improving upon previous work on the subject, we use Wright's Circle Method to derive an asymptotic formula for the number of parts in all partitions of an integer that are in any given arithmetic progression.
We investigate some asymptotic properties of extrema to a two-dimensional variational problem in the unit disk. Some results about non-radialicity of solutions are given.
We study the enumeration problem of higher dimensional partitions, a natural generalisation of classical integer partitions. We show that their counting problem is equivalent to the enumeration of simpler classes of higher dimensional…
We prove a version of the countable union theorem for asymptotic dimension and we apply it to groups acting on asymptotically finite dimensional metric spaces. As a consequence we obtain the following finite dimensionality theorems. A) An…
In this work we present the details of calculations we previously performed for the large j behavior of certain 3j and coefficients. We compare exact and asymptotic expressions.