Related papers: A topological framework for signed permutations
We introduce and investigate a novel notion of transversely affine foliation, comparing and contrasting it to the previous ones in the literature. We then use it to give an extension of the classic Hadamard's theorem from Riemannian…
In this paper, we introduce two new forms of the dual Hartwig-Spindelb{\"o}ck decomposition and employ them to derive explicit representations for several classes of dual generalized inverses. Building on these representations, we further…
Using the shuffle structure of the graphs, we introduce a new kind of the Hopf algebraic structure for tagged graphs with, or without loops. Like a quantum group structure, its product is non-commutative. With the help of the Hopf algebraic…
Contracting the $h$-deformation of $\SL(2,\Real)$, we construct a new deformation of two dimensional Poincar\'e algebra, the algebra of functions on its group and its differential structure. It is also shown that the Hopf algebra is…
The Witten $r$-spin class defines a non-semisimple cohomological field theory. Pandharipande, Pixton and Zvonkine studied two special shifts of the Witten class along two semisimple directions of the associated Dubrovin--Frobenius manifold…
The signed permutation modules are a simultaneous generalization of the ordinary permutation modules and the twisted permutation modules of the symmetric group. In a recent paper Dave Benson and Peter Symonds defined a new invariant…
Let $\pi=(\pi_1,\pi_2,\hdots,\pi_n)$ be permutation of the elements $1,2,\hdots,n. $ Positive integer $k\leq2^{n-1}$ we call index of $\pi,$ if in its binary notation as $n$-digital binary number, the 1's correspond to the ascent points. We…
The inverse problem of fractional Brownian motion and other Gaussian processes with stationary increments involves inverting an infinite hermitian positively definite Toeplitz matrix (a matrix that has equal elements along its diagonals).…
A signed permutation \pi = \pi_1\pi_2 \ldots \pi_n in the hyperoctahedral group B_n is a word such that each \pi_i \in {-n, \ldots, -1, 1, \ldots, n} and {|\pi_1|, |\pi_2|, \ldots, |\pi_n|} = {1,2,\ldots,n}. An index i is a peak of \pi if…
We expound on some known lower bounds of the quadratic Wasserstein distance between random vectors in $\mathbb{R}^n$ with an emphasis on affine transformations that have been used in manifold learning of data in Wasserstein space. In…
We investigate a quantum geometric space in the context of what could be considered an emerging effective theory from Quantum Gravity. Specifically we consider a two-parameter class of twisted Poincar\'e algebras, from which Lie-algebraic…
The problem of genealogy of permutations has been solved partially by Stefan (odd order) and Acosta-Hum\'anez \& Bernhardt (power of two). It is well known that Sharkovskii's theorem shows the relationship between the cardinal of the set of…
We study an inverse problem on a finite connected graph G = (X, E), on whose vertices a conductivity {\gamma} is defined. Our data consists in a sequence of partial observations of a fractional random walk on G. The observations are partial…
We describe three ways of modifying the relativistic Heisenberg algebra - first one not linked with quantum symmetries, second and third related with the formalism of quantum groups. The third way is based on the identification of…
We present a framework which unifies a large class of non-commutative spacetimes that can be described in terms of a deformed Heisenberg algebra. The commutation relations between spacetime coordinates are up to linear order in the…
The interplay between topological localization and non-Hermiticity localization in non-Hermitian crystal systems results in a diversity of shapes of topological edge modes (EMs), offering opportunities to manipulate these modes for…
We study unparametrized conformal circles, or called conformal geodesics, study diffeomorphisms mapping conformal circles to conformal circles in pseudo-Riemannian conformal manifolds. We show that such local diffeomorphisms are conformal…
Twisted homomorphisms of bialgebras are bialgebra homomorphisms from the first into Drinfeld twistings of the second. They possess a composition operation extending composition of bialgebra homomorphisms. Gauge transformations of twists,…
Using zippered rectangle coordinates we parametrize a Poincar\'e section for horocycle flow on the space of genus 2 translation surfaces with one singular cone point of angle $6\pi$. In addition, we bound the return time under horocycle…
We demonstrate the existence of an open set of data which exhibits \textit{reversal} and \textit{recirculation} for the stationary Prandtl equations (data is taken in an appropriately defined product space due to the simultaneous forward…