Related papers: Necessary Conditions for Schur-Positivity

We define a number of related combinatorial objects, each of which possesses a surprising symmetry. We include several applications such as a combinatorial explanation for certain fixed points of the involution $\omega$ on the ring of…

In this note, necessary and sufficient conditions are obtained for unilateral weighted shifts to be near subnormal . As an application of the main results, many answers to the Hilbert space problem 160 are presented at the end of the paper.

Schur's test states that if $K:X\times Y\to\mathbb{C}$ satisfies $\int_Y |K(x,y)|d\nu(y)\leq C$ and $\int_X |K(x,y)|d\mu(x)\leq C$, then the associated integral operator acts boundedly on $L^p$ for all $p\in [1,\infty]$. We derive a variant…

Let $E$ be a vector bundle and $S_a$, $S_b$ the Schur functors associated to partitions $a$ and $b$. Previously we have shown that ampleness of $S_aE$ implies ampleness of $S_bE$ when $a$ is greater than $b$ in the dominance partial order.…

We give a necessary and sufficient condition for existence of spinc structures on real Bott manifolds.

For a line bundle L on a smooth surface S, it is now known that the degree of the Severi variety of cogenus-d curves is given by a universal polynomial in the Chern classes of L and S if L is d-very ample. For S rational, we relax the…

Using differential subordination technique, such as Briot-Bouquet and others, we establish sufficient conditions for functions to be in a class $\mathcal{S}^{*}_{\varrho},$ consisting of starlike functions that are associated with…

Classical conditions for ensuring the robust stability of a linear system in feedback with a sector-bounded nonlinearity include small gain, circle, passivity, and conicity theorems. In this work, we present a similar stability condition,…

In [19] there is an approach to the investigation of the pseudocontinuability of Schur functions in terms of Schur parameters. In particular, there was obtained a criterion for the pseudocontinuability of Schur functions and the Schur…

We introduce an operational criterion to identify Wigner function (WF) negativity for an arbitrary quantum state within the framework of quantum non-demolition measurements. This criterion corresponds to experimentally accessible schemes…

We prove a formula for the image of a skew Schur polynomial $s_{\lambda/\mu}\left( x_{1}, x_{2}, \ldots, x_{N}\right) $ under the differential operator $\nabla:= \dfrac{\partial}{\partial x_{1}} +\dfrac{\partial}{\partial…

Let $\{h_1,h_2,...\}$ be a set of algebraically independent variables. We ask which vectors are extreme in the cone generated by $h_ih_j-h_{i+1}h_{j-1}$ ($i\geq j>0$) and $h_i$ ($i>0$). We call this cone the cone of log concavity. More…

The stability requirements for a noncommutative scalar field coupled to gravity is investigated through the positive energy theorem. It is shown that for a noncommutative scalar with a polynomial potential, the stability conditions are…

In this paper, we give a necessary and sufficient condition for an even order three dimensional strongly symmetric circulant tensor to be positive semi-definite. In some cases, we show that this condition is also sufficient for this tensor…

We provide necessary and sufficient geometric conditions for the exact observability of the Schr\"odinger equation with inverse-square potentials on the half-line. These conditions are derived from a Logvinenko-Sereda type theorem for…

Let $A_{1}$, $A_{2}$, $...$, $A_{k}$ be strictly positive operators on a Hilbert space. This note is to show a sufficient condition of $A_{k}\geq A_{k-1}\geq\geq A_{3}\geq A_{2}\geq A_{1}$, which extends the related result before.

We provide the special values of the skew version of the $K$-theoretic Schur $P$- and $Q$-functions. Using these special values, we show an oddness property of the number of shifted set-valued skew tableaux. Additionally, we generalize…

Recently, in [18] the authors gave some results on the structure, capability and the Schur multiplier of generalized Heisenberg Lie superalgebra. In this work we try to extend these concepts to the case of generalized Heisenberg Lie…

We obtain a set of necessary and sufficient conditions for $| \bar{N}, p_{n} |_{k} $ to imply $|\bar{N}, q_{n} |_{s}$ for $1 < k \leq s < \infty$. Using this result we establish several inclusion theorems as well as conditions for the…

The question of classifying when two skew Schur functions are equal is a substantial open problem, which remains unsolved for over a century. In 2022, Aliniaeifard, Li and van Willigenburg introduced skew Schur functions in noncommuting…