Related papers: Permutations with only reduced co-BPDs
The boolean elements of a Coxeter group have been characterized and shown to possess many interesting properties and applications. Here we introduce "prism permutations," a generalization of those elements, characterizing the prism…
The space $QSym_n(B)$ of $B$-quasisymmetric polynomials in 2 sets of $n$ variables was recently studied by Baumann and Hohlweg. The aim of this work is a study of the ideal $<QSym_n(B)^+>$ generated by $B$-quasisymmetric polynomials without…
We discuss relations between quantum BPS invariants defined in terms of a product decomposition of certain series, and difference equations (quantum A-polynomials) that annihilate such series. We construct combinatorial models whose…
We increase the scope of previous work on change of basis between finite bases of polynomials by defining ascending and descending bases and introducing three techniques for defining them from known ones. The minimum degrees of polynomials…
The Cauchy identity gives a recipe for decomposing a double Grothendieck polynomial $\mathfrak{G}^{(\beta)}_w(x;y)$ as a sum of products $\mathfrak{G}^{(\beta)}_v(x)\mathfrak{G}^{(\beta)}_u(y)$ of single Grothendieck polynomials.…
In this work, tests of symmetry for bivariate copulas are introduced and studied using empirical Bernstein copula process. Three statistics are proposed and their asymptotic properties are established. Besides, a multiplier bootstrap…
The problem of covering a region of the plane with a fixed number of minimum-radius identical balls is studied in the present work. An explicit construction of bi-Lipschitz mappings is provided to model small perturbations of the union of…
A bifibration structure on a $6$-manifold is a map to either the complex projective plane $\mathbb{P}^2$ or a $\mathbb{P}^1$-bundle over $\mathbb{P}^1$, such that its composition with the projection to $\mathbb{P}^1$ is a ($6$-dimensional)…
Shifted partial derivative (SPD) methods are a central algebraic tool for circuit lower bounds, measuring the dimension of spaces of shifted derivatives of a polynomial. We develop the Shifted Partial Derivative Polynomial (SPDP) framework,…
This paper provides a systematic study of fundamental combinatorial properties of one-dimensional, two-sided infinite simple Toeplitz subshifts. Explicit formulas for the complexity function, the palindrome complexity function and the…
Permutation of any two hidden units yields invariant properties in typical deep generative neural networks. This permutation symmetry plays an important role in understanding the computation performance of a broad class of neural networks…
We present new alternative complete asymptotic expansions for the time harmonic low--frequency magnetic field perturbation caused by the presence of a conducting permeable object as its size tends to zero for the eddy current approximation…
This paper proposes seven combinatorial problems around formulas for the characteristic polynomial and the spectral numbers of a quasihomogeneous singularity. One of them is a new conjecture on the characteristic polynomial. It is an…
We introduce a variation of the well-known Newton-Hironaka polytope for algebroid hypersurfaces. This combinatorial object is a perturbed version of the original one, parametrized by a real number. For well-chosen values of the parameter,…
We study the BPS invariants of the preferred Calabi-Yau resolution of ADE polyhedral singularities C^3/G given by Nakamura's G-Hilbert schemes. Genus 0 BPS invariants are defined by means of the moduli space of torsion sheaves as proposed…
The Poisson multi-Bernoulli mixture (PMBM) is a multi-object conjugate prior for the closed-form Bayes random finite sets filter. The extended object PMBM filter provides a closed-form solution for multiple extended object filtering with…
Shallow permutations were defined in 1977 to be those that satisfy the lower bound of the Diaconis-Graham inequality. Recently, there has been renewed interest in these permutations. In particular, Berman and Tenner showed they satisfy…
Blind deconvolution (BD) arises in many applications. Without assumptions on the signal and the filter, BD does not admit a unique solution. In practice, subspace or sparsity assumptions have shown the ability to reduce the search space and…
We propose a unified approach to a general class of codimension-2 defects in field theories with non-trivial duality symmetries and discuss various constructions of such "duality defects" in diverse dimensions. In particular, in d=4 we…
In recent years, various nonlinear algebraic structures have been obtained in the context of quantum systems as symmetry algebras, Painlev\'{e} transcendent models and missing label problems. In this paper we treat all of these algebras as…