Related papers: Growth problems in diagram categories
We introduce and validate an algorithm to compute transient amplication factors for the Orr-Sommerfeld-Squire linear theory for parallel two-phase flow. We further introduce direct numerical simulation as a way of comparing the linear…
Recent work has shown a deep connection between semilocal approximations in density functional theory and the asymptotics of the sum of the WKB semiclassical expansion for the eigenvalues. However, all examples studied to date have…
Regular and singular parts of asymptotic expansions of semi-Markov random evolutions are given. Regularity of boundary conditions is shown. An algorithm for calculation of initial conditions is proposed.
We present new algorithm for growth of non-clustered planar graphs by aggregation of cells with given distribution of size and constraint of connectivity k=3 per node. The emergent graph structures are controlled by two parameters--chemical…
We investigate products of certain double cosets for the symmetric group and use the findings to derive some multiplication formulas for q-Schur superalgebras. This gives a combinatorialisation of the relative norm approach developed by the…
We derive asymptotic formulae for the coefficients of bivariate generating functions with algebraic and logarithmic factors. Logarithms appear when encoding cycles of combinatorial objects, and also implicitly when objects can be broken…
The asymptotic nature of perturbative expansions in quantum field theory can arise from the factorial growth in the number of Feynman diagrams with loop order, as with instantons, or from a series of individual diagrams whose values grow…
We derive an asymptotic expansion for the distribution of a compound sum of independent random variables, all having the same light-tailed subexponential distribution. The examples of a Poisson and geometric number of summands serve as an…
An asymptotic formula for the number of partitions into p-cores is derived. As a byproduct some integer valued trigonometric sums are found
We establish asymptotic formulas for sums of reciprocals of primes in arithmetic progressions, generalizing recent results on multiple Mertens evaluations by Tenenbaum, Qi, and Hu. Specifically, for any fixed constant $K>0$, we derive…
In a previous work (arXiv:2505.05574), a summation formula for harmonic Maass forms of polynomial growth was established. In this note, we use the theory of $L$-series of harmonic Maass forms to state and prove a summation formula for such…
We present a survey of results related to the Milnor's problem on group growth. We discuss the cases of polynomial growth, exponential but not uniformly exponential growth, but the main part of the article is devoted to the intermediate…
Asymptotic expansions for a wide class of distribution are studied. A simple method for computation of the series coefficients is suggested. The case when regularization parameter of the distribution depends on the asymptotic parameter is…
We introduce and study several affine (=annular in this paper) versions of the classical diagram algebras such as Temperley-Lieb, partition, Brauer, Motzkin, rook Brauer, rook, planar partition, and planar rook algebras. We give generators…
In this note we give asymptotic estimates for the volume growth associated to suitable infinite graphs. Our main application is to give an asymptotic estimate for volume growth associated to translation surfaces.
We obtain an asymptotic expansion for $p(n)$, the number of partitions of a natural number $n$, starting from a formula that relates its generating function $f(t), t\in (0,1)$ with the characteristic functions of a family of sums of…
We give asymptotic expressions for the number of commuting matrices over finite fields. For this, we use product expansions for the corresponding generating functions.
Consensus is a well-studied problem in distributed sensing, computation and control, yet deriving useful and easily computable bounds on the rate of convergence to consensus remains a challenge. This paper discusses the use of seminorms for…
For a large integer $m,$ we obtain an asymptotic formula for the number of solutions of a certain congruence modulo $m$ with four variables, where the variables belong to special sets of residue classes modulo $m.$ This formula are applied…
Let $\sum_{\beta\in\nats^d} F_\beta x^\beta$ be a multivariate power series. For example $\sum F_\beta x^\beta$ could be a generating function for a combinatorial class. Assume that in a neighbourhood of the origin this series represents a…