Related papers: Growth problems in diagram categories
We give explicit formulas for the asymptotic growth rate of the number of summands in tensor powers in certain monoidal categories with finitely many indecomposable objects, and related structures.
We give a general asymptotic formula for the growth rate of the number of indecomposable summands in the tensor powers of representations of finite groups, over a field of arbitrary characteristic. In characteristic zero we obtain…
We discuss formulas for the asymptotic growth rate of the number of summands in tensor powers in certain (finite or infinite) monoidal categories. Our focus is on monoidal categories with infinitely many indecomposable objects, with our…
In this paper we study the asymptotic behavior of the number of summands in tensor products of finite dimensional representations of affine (semi)group (super)schemes and related objects.
We give a conjecture for the asymptotic growth rate of the number of indecomposable summands in the tensor powers of representations of finite monoids, expressing it in terms of the (Brauer) character table of the monoid's group of units.…
The algebraic properties of formal power series, whose coefficients show factorial growth and admit a certain well-behaved asymptotic expansion, are discussed. It is shown that these series form a subring of $\mathbb{R}[[x]]$. This subring…
Tensor products of quiver representations have been extensively studied; typical examples include the pointwise tensor product and the tensor product induced by the coalgebra structure of path algebras. In this paper, we investigate the…
We study new asymptotic invariant of a pair consisting of a group and a subgroup, which we call Commensurizer Growth. We compute the commensurizer growth for several examples, concentrating mainly on the case of a locally compact…
We construct an increasing, submultiplicative, arbitrarily rapid function which is not equivalent to the growth function of any finitely generated algebra, demonstrating the difficulty in characterizing growth functions in an asymptotic…
We study the asymptotic size of decompositions of tensor powers of tilting modules for quantum groups (mostly at a complex root of unity). In type A1 we obtain a sharp result for the number of indecomposable summands, explained by a one…
Given a finite-dimensional representation $V$ over an algebraically closed field of an abstract group $G$, we consider the number of the trivial summand counted with multiplicity in the direct sum decomposition of $V^{\otimes n}$. We give…
We propose a graphical language that accommodates two monoidal structures: a multiplicative one for pairing and an additional one for branching. In this colored PROP, whether wires in parallel are linked through the multiplicative structure…
We consider semisimple super Tannakian categories generated by an object whose symmetric or alternating tensor square is simple up to trivial summands. Using representation theory, we provide a criterion to identify the corresponding…
This paper concerns the asymptotic behaviour of solutions of a linear convolution Volterra summation equation with an unbounded forcing term. In particular, we suppose the kernel is summable and ascribe growth bounds to the exogenous…
We investigate the problem of the distribution of sums of functions of prime numbers located on an arithmetic progression. This problem is closely related to the problem of the distribution of prime numbers on an arithmetic progression.…
When k > 1 and s is sufficiently large in terms of k, we derive an explicit multi-term asymptotic expansion for the number of representations of a large natural number as the sum of s positive integral k-th powers.
We enumerate the connected graphs that contain a number of edges growing linearly with respect to the number of vertices. So far, only the first term of the asymptotics and a bound on the error were known. Using analytic combinatorics, ie…
We determine the possible functions that can occur, up to asymptotic equivalence, as growth functions of semigroups, hereditary languages, and algebras.
General results on asymptotic expansions of Feynman diagrams in momenta and/or masses are reviewed. It is shown how they are applied for calculation of massive diagrams.
We give a description of non-growing subsets in linear groups, which extends the Product theorem for simple groups of Lie type. We also give an account of various related aspects of growth in linear groups.