Related papers: On the growth of the Kronecker coefficients
The reduced Kronecker coefficients are particular instances of Kronecker coefficients that contain enough information to recover them. In this notes we compute the generating function of a family of reduced Kronecker coefficients. We also…
We take a data-scientific approach to study whether Kronecker coefficients are zero or not. Motivated by principal component analysis and kernel methods, we define loadings of partitions and use them to describe a sufficient condition for…
We present a way of computing Kronecker coefficients that uses a new family of rational convex polytopes, called column-row polytopes. We give several different formulas for the computation. They are alternating sums of numbers of integer…
We present a study of three families of Kronecker coefficients, which we describe in terms of reduced Kronecker coefficients. This study is grounded on the generating function of the coefficients, proved by a bijection between two…
We look at the rate of growth of the partial quotients of the infinite continued fraction expansion of an irrational number relative to the rate of approximation of the number by its convergents. In non-generic cases the Hausdorff dimension…
We show that rectangular Kronecker coefficients stabilize when the lengths of the sides of the rectangle grow, and we give an explicit formula for the limit values in terms of invariants of $\fsl_n$.
We review models of compositional growth, which were introduced to explain the growth statistics of various quantities ranging from firm sizes to GDP. In these models, entities are decomposed into units that grow independently. Thus, the…
The Kronecker coefficients are the structure constants for the restriction of irreducible representations of the general linear group $GL(n m)$ into irreducibles for the subgroup $GL(n)\times GL(m)$. In this work we study the…
We construct bases of the simple modules for partition algebras which are indexed by paths in an alcove geometry. This allows us to give a concrete interpretation (and new proof) of the monotone convergence property for Kronecker…
Mathematical structure of the reflection coefficients for the one-dimensional Fokker-Planck equation is studied. A new formalism using differential operators is introduced and applied to the analysis in high- and low-energy regions.…
An extension of coupled maps is given which allows for the growth of the number of elements, and is inspired by the cell differentiation problem. The growth of elements is made possible first by clustering the phases, and then by…
Understanding how growth induces form is a longstanding biological question. Many studies concentrated on the shapes of plant cells, fungi or bacteria. Some others have shown the importance of the mechanical properties of bacterial walls…
Cell growth in size is a complex process coordinated by intrinsic and environmental signals. In a recent work [Tzur et al., Science, 2009, 325:167-171], size distributions in an exponentially growing population of mammalian cells were used…
The computation of Kronecker coefficients is a challenging problem with a variety of applications. In this paper we present an approach based on methods from symplectic geometry and residue calculus. We outline a general algorithm for the…
Growth-fragmentation processes model systems of cells that grow continuously over time and then fragment into smaller pieces. Typically, on average, the number of cells in the system exhibits asynchronous exponential growth and, upon…
We investigate the rate of growth of the function of n which counts the number of complex irreducible representations of a fixed group of degree less than or equal to n. The emphasis is on linear groups, especially compact real and p-adic…
The growth rate of organisms depends both on external conditions and on internal states, such as the expression levels of various genes. We show that to achieve a criterion mean growth rate over an ensemble of conditions, the internal…
We develop a Fokker-Planck theory of tissue growth with three types of cells (symmetrically dividing, asymmetrically dividing and non-dividing) as main agents to study the growth dynamics of human cerebral organoids. Fitting the theory to…
It is widely believed that the particular wiring observed within cortical columns boosts neural computation. We use rewiring of neural networks performing real-world cognitive tasks to study the validity of this argument. In a vast survey…
We investigate a class of Young diagrams growing via the addition of unit cells and satisfying the constraint that the height difference between adjacent columns $\geq r$. In the long time limit, appropriately re-scaled Young diagrams…