Related papers: New Wilf-equivalence results for dashed patterns

Edgeworth expansions of first and second order are established for general linear rank statistics under the null hypothesis with asymptotically ''sufficiently'' small remainder terms. The methods used are the Stein method combined with an…

Inspired by a recent pointwise differential inequality for positive bounded solutions of the fourth-order H\'enon equation $\Delta^2 u = |x|^a u^p$ in ${\mathbb R}^n$ with $a \geqslant 0$, $p > 1$, $n \geqslant 5$ due to Fazly, Wei, and Xu…

For each infinite series of the classical Lie groups of type B,C or D, we introduce a family of polynomials parametrized by the elements of the corresponding Weyl group of infinite rank. These polynomials represent the Schubert classes in…

In this paper, we first review Huei's formulation in which it is shown that the linearized Einstein equations can be written in the same form as the Maxwell equations. We eliminate some imperfections like the scalar potential which is ill…

We use Pitt inequalities for the Fourier transform to prove the following weighted gradient inequality $$ \|e^{-\tau\ell(\cdot)} u^{\frac 1q} f\|_q\leq c_\tau\| e^{-\tau\ell(\cdot)} v^{\frac 1p}\, \nabla f\|_p, \quad f\in C^\infty_0( R^n).…

The purpose of this article is to present one and two-weight inequalities for bilinear multiplier operators in Dunkl setting with multiple Muckenhoupt weights. In order to do so, new results regarding Littlewood-Paley type theorems and…

Let $f$ be a newform of weight $k\geq 2$, level $N$ with coefficients in a number field $K$, and $A$ the adjoint motive of the motive $M$ associated to $f$. We carefully discuss the construction of the realisations of $M$ and $A$, as well…

We prove the existence of similar and multi-similar point configurations (or simplexes) in sets of fractional Hausdorff measure in Euclidean space. These results can be viewed as variants, for thin sets, of theorems for sets of positive…

This paper introduces a novel quasi-likelihood extension of the generalised Kendall \(\tau_{a}\) estimator, together with an extension of the Kemeny metric and its associated covariance and correlation forms. The central contribution is to…

We prove a duality theorem for the $p$-adic etale motivic cohomology of a variety $U$ which is the complement of a divisor on a smooth projective variety over $\F_p$. This extends the duality theorems of Milne and Jannsen-Saito-Zhao. The…

In this paper we investigate the well-posedness of backward or forward stochastic differential equations whose law is constrained to live in an a priori given (smooth enough) set and which is reflected along the corresponding ''normal''…

We study sorting operators $\mathbf{A}$ on permutations that are obtained composing Knuth's stack sorting operator $\mathbf{S}$ and the reversal operator $\mathbf{R}$, as many times as desired. For any such operator $\mathbf{A}$, we provide…

Submodular functions are known to satisfy various forms of fractional subadditivity. This work investigates the conditions for equality to hold exactly or approximately in the fractional subadditivity of submodular functions. We establish…

This paper gives necessary and sufficient conditions for the convergence of the solution of a weakly damped second order linear differential equation that is subjected to outside forcing, for which solutions of the unforced equation are…

We consider a Kendall's tau measure between a binary group indicator and the continuous variable under investigation to develop a thorough two-sample comparison procedure. The measure serves as a useful alternative to the hazard ratio whose…

In the work the fair division problem for two participants in presence of both divisible and indivisible items is considered. The set of all divisions is formally described; it is demonstrated that fair (in terms of Brams and Taylor)…

In this paper we propose an alternative to the coupling of Berkes, Liu and Wu [1] to obtain strong approximations for partial sums of dependent sequences. The main tool is a new Rosen-thal type inequality expressed in terms of the coupling…

We introduce and study a notion of duality for two classes of optimization problems commonly occurring in probability theory. That is, on an abstract measurable space $(\Omega,\mathcal{F})$, we consider pairs $(E,\mathcal{G})$ where $E$ is…

We give a direct combinatorial proof of the equidistribution of two pairs of permutation statistics, (des, aid) and (lec, inv), which have been previously shown to have the same joint distribution as (exc, maj), the major index and the…

We establish a Liouville comparison principle for entire weak sub- and super-solutions of the equation $(\ast)$ $w_t-\Delta_p (w) = |w|^{q-1}w$ in the half-space ${\mathbb S}= {\mathbb R}^1_+\times {\mathbb R}^n$, where $n\geq 1$, $q>0$ and…