Related papers: A note on generating functions

This is a note for constructing fundamental invariants and computing the Hilbert series of the invariant subalgebras of tensor products of polynomial rings under the action by a direct product of symmetric groups. Our computation relies on…

Many groups possess highly symmetric generating sets that are naturally endowed with an underlying combinatorial structure. Such generating sets can prove to be extremely useful both theoretically in providing new existence proofs for…

We describe generating functions for arbitrary-genus Gromov-Witten invariants of the projective space with any number of marked points explicitly. The structural portion of this description gives rise to uniform energy bounds and vanishing…

We propose a new class of generative diffusion models, called functional diffusion. In contrast to previous work, functional diffusion works on samples that are represented by functions with a continuous domain. Functional diffusion can be…

For every affine variety over a global function field, we show that the set of its points with coordinates in an arbitrary rank-one multiplicative subgroup of this function field is topologically dense in the set of its points with…

We describe a technique for constructing a symplectic transfer map for a charged particle moving through an accelerator component with arbitrary three-dimensional static magnetic field. The transfer map is constructed by symplectic…

We prove that every smooth subelliptic variety admits a surjective morphism from an affine space. This result gives partial answers to the questions of Arzhantsev and Forstneri\v{c}. As an application, we characterize open images of…

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…

We construct a symplectic structure on a disc that admits a compactly supported symplectomorphism which is not smoothly isotopic to the identity. The symplectic structure has an overtwisted concave end; the construction of the…

In this note we survey recent results on automorphisms of affine algebraic varieties, infinitely transitive group actions and flexibility. We present related constructions and examples, and discuss geometric applications and open problems.

We introduce floating bodies for convex, not necessarily bounded subsets of $\mathbb{R}^n$. This allows us to define floating functions for convex and log concave functions and log concave measures. We establish the asymptotic behavior of…

Certain classical generating functions for elements of reflection groups can be expressed using fundamental invariants called exponents. We give new analogues of such generating functions that accommodate orbits of reflecting hyperplanes…

Given a finite graded poset with labeled Hasse diagram, we construct a quasi- symmetric generating function for (saturated) chains whose labels have fixed descents. This is a common generalization of a generating function for the flag…

A solution is proposed for the problem of composition of ordinary generating functions. A new class of functions that provides a composition of ordinary generating functions is introduced; main theorems are presented; compositae are written…

We analyse the asymptotic symmetries of Maxwell theory at spatial infinity through the Hamiltonian formalism. Precise, consistent boundary conditions are explicitly given and shown to be invariant under asymptotic angle-dependent…

The generating function for the orbifold Euler characteristic of the moduli space of real algebraic curves of genus $2g$ (locally orientable surfaces) with $n$ marked points $\chi^r(\mathfrak{M}_{2g,n})$, is identified with a simple…

Let (M,w,L) be a symplectic manifold endowed with a lagrangian foliation L. Liberman and Weinstein have shown that the leaves of L are endowed with an affine structure. In this paper we provide links between the theories of affine manifolds…

There has been a certain interest in some recent works in the derivation of Noether charges for Hopf-algebra space-time symmetries. Such analyses relied rather heavily on delicate manipulations of the fields of non-commuting coordinates…

Introducing a quaternionic structure on Euclidean space, the fundaments for quaternionic and symplectic Clifford analysis are studied in detail from the viewpoint of invariance for the symplectic group action.

The mathematical theory underlying Hamiltonian mechanics is called symplectic geometry. So symplectic geometry arose from the roots of mechanics and is seen as one of the most valuable links between physics and mathematics today. Symplectic…