Related papers: Commuting Eulerian operators
In this paper we present an explicit formula for the number of permutations with a given number of alternating descents. Moreover, we study the interlacing property of the real parts of the zeros of the generating polynomials of these…
We give a new combinatorial interpretation of the stationary distribution of the (partially) asymmetric exclusion process on a finite number of sites in terms of decorated alternative trees and colored permutations. The corresponding…
A particular case of [07] was generalized from contractions to polynomially bounded operators in [G19]. Namely, it is proved in [G19] that if the unitary asymptote of a polynomially bounded operator $T$ contains the bilateral shift of…
The aim of this paper is to study degenerate Eulerian polynomials and degenerate Eulerian numbers, respectively as degenerate versions of the Eulerian polynomials and the Eulerian numbers, and to derive some of their properties.…
We consider the spectrum of a two-dimensional Pauli operator with a compactly supported electric potential and a variable magnetic field with a positive mean value. The rate of accumulation of eigenvalues to zero is described in terms of…
By normalizing the space of commuting pairs of elements in a reductive Lie group G, and the corresponding space for the Langlands dual group, we construct pairs of hyperkahler orbifolds which satisfy the conditions to be mirror partners in…
In this work, the commutator of any two reasonable functions of several pairs of canonical conjugate operators is obtained as a sum of terms of partial derivatives of those functions (equations 9, 10 or 11). When applied to quantum…
We characterize bifurcation values of polynomial functions by using the theory of perverse sheaves and their vanishing cycles. In particular, by introducing a method to compute the jumps of the Euler characteristics with compact support of…
Motivated by the Poisson Dixmier-Moeglin equivalence problem, a systematic study of commutative unitary rings equipped with a {\em biderivation}, namely a binary operation that is a derivation in each argument, is here begun, with an eye…
We indicate smooth real commuting matrix differential operators whose eigenvalues and eigenfunctions are parametrized by two-dimensional principally polarized abelian varieties.
This paper is motivated by determining the location of modes of some unimodal Eulerian-type polynomials. The notion of ratio monotonicity was introduced by Chen-Xia when they investigated the $q$-derangement numbers. Let…
For an inner function u we discuss the dual operator for the well-known compressed shift. We establish conditions for two dual compressed shifts to be unitarily equivalent/similar and we describe the invariant subspace structure for the…
In this paper we study extensions of commuting tuples of symmetric and isometric operators to commuting tuples of self-adjoint and unitary operators. Some conditions which ensure the existence of such extensions are presented. A…
Led by the key example of the Korteweg-de Vries equation, we study pairs of Hamiltonian operators which are non-homogeneous and are given by the sum of a first-order operator and an ultralocal structure. We present a complete classification…
We compute explicit formulas for the curvature operators and Poincar\'e polynomials of all compact irreducible symmetric spaces. We can easily derive the Poincar\'e polynomials using quantum numbers, giving a formula that mirrors the known…
Permutation tableaux are combinatorial objects related with permutations and various statistics on them. They appeared in connection with total positivity in Grassmannians, and stationary probabilities in a PASEP model. In particular they…
The Bayesian approach to ill-posed operator equations in Hilbert space recently gained attraction. In this context, and when the prior distribution is Gaussian, then two operators play a significant role, the one which governs the operator…
The alternating descent statistic on permutations was introduced by Chebikin as a variant of the descent statistic. We show that the alternating descent polynomials on permutations are unimodal via a five-term recurrence relation. We also…
We consider expressions of the form of an exponential of the sum of two non-commuting operators of a single variable inside a path integration. We show that it is possible to shift one of the non-commuting operators from the exponential to…
This work establishes a multivariable Wold-type decomposition for left-inverse commuting $n$-tuples of bounded operators, built on the hypothesis that each component admits a Wold-type decomposition. For pairs of operators, we obtain a…