Related papers: Palindromic permutations and generalized Smarandac…
Let $G$ be a group with involution * and $\sigma\colon G\to\{\pm1\}$ a group homomorphism. The map $\sharp$ that sends $\alpha=\sum\alpha_gg$ in a group ring $RG$ to $\alpha^{\sharp}=\sum\sigma(g)\alpha_gg^*$ is an involution of $RG$ called…
Surface plasmon polariton (SPP) as a bounded mode on a metal/dielectric interface intrinsically has a definite transverse magnetic (TM) polarization that usually lacks further manipulations. However, the in-plane longitudinal components of…
Three-dimensional N-extended superconformal symmetry is studied within the superspace formalism. A superconformal Killing equation is derived and its solutions are classified in terms of supertranslations, dilations, Lorentz…
We study the spectral properties of a class of random matrices of the form $S_n^{-} = n^{-1}(X_1 X_2^* - X_2 X_1^*)$ where $X_k = \Sigma^{1/2}Z_k$, for $k=1,2$, $Z_k$'s are independent $p\times n$ complex-valued random matrices, and…
Orientably-regular maps are highly symmetric embeddings of graphs in oriented surfaces. Among them, chiral maps are those which fail to be isomorphic to their mirror images. We prove that, as $n\to\infty$, chirality is generic for…
The spherical Radon-Dunkl transform $R_\kappa$, associated to weight functions invariant under a finite reflection group, is introduced, and some elementary properties are obtained in terms of $h$-harmonics. Several inversion formulas of…
We provide a family of representations of GL(2n) over a p-adic field that admit a non-vanishing linear functional invariant under the symplectic group (i.e. representations that are Sp(2n)- distinguished). While our result generalizes a…
The pancake problem is concerned with sorting a permutation (a stack of pancakes of different diameter) using only prefix reversals (spatula flips). Although the problem description belies simplicity, an exact formula for the maximum number…
For a unital ring $S$, an $S$-linear quasigroup is a unital $S$-module, with automorphisms $\rho$ and $\lambda$ giving a (nonassociative) multiplication $x\cdot y=x^\rho+y^\lambda$. If $S$ is the field of complex numbers, then ordinary…
We classify all possible charge lattices and 1-form symmetry groups for $\mathcal{N}=2$ SCFTs with characteristic dimension $\varkappa \neq \{1,2\}$. For rank-$r$ SCFTs that are not stacks of lower rank theories the order of the 1-form…
In this paper, we study symmetric lattice paths. Let $d_{n}$, $m_{n}$, and $s_{n}$ denote the number of symmetric Dyck paths, symmetric Motzkin paths, and symmetric Schr\"oder paths of length $2n$, respectively. By using Riordan group…
Using a recursive algorithm to solve the renormalization group equations of N=1 QCD (DGLAP), we describe the most general supersymmetric evolution of the parton distributions. The analysis involves the regular DGLAP evolution, a partial…
Recently, Babson and Steingrimsson (see \cite{BS}) introduced generalized permutations patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. In this paper we study the generating…
This is a continuation of the expository article \cite{krp} with some new remarks. Let $S_n$ denote the set of all Gaussian states in the complex Hilbert space $L^2 (\mathbb{R}^n),$ $K_n$ the convex set of all momentum and position…
We show that two involutions on the variety $N_n^+$ of upper triangular totally positive matrices are related, on the one hand, to the tetrahedron equation and, on the other hand, to the action of the symmetric group $S_3$ on some…
Transformation optics has recently attracted extensive interest, since it provides a novel design methodology for manipulating light at will. Although transformation optics in principle embraces all forms of electromagnetic phenomena on all…
For recursively generated shifts, we provide definitive answers to two outstanding problems in the theory of unilateral weighted shifts: the Subnormality Problem ({\bf SP}) (related to the Aluthge transform) and the Square Root Problem…
The renormalization group is the cornerstone of the modern theory of universality and phase transitions, a powerful tool to scrutinize symmetries and organizational scales in dynamical systems. However, its network counterpart is…
Relativistic massive Lorentz electrodynamics (LED) is studied in a ``gyroscopic setup'' where the electromagnetic fields and the particle spin are the only dynamical degrees of freedom. A rigorous proof of the global existence and…
Let PL+(S1) be the group of order preserving piecewise linear homeomorphisms of the circle. An element in PL+(S1) is called reversible in PL+(S1) if it is conjugate to its inverse in PL+(S1). We characterize the reversible elements in…