A Unified Elementary Approach to the Dyson, Morris, Aomoto, and Forrester Constant Term Identities

We introduce an elementary method to give unified proofs of the Dyson, Morris, and Aomoto identities for constant terms of Laurent polynomials. These identities can be expressed as equalities of polynomials and thus can be proved by verifying them for sufficiently many values, usually at negative integers where they vanish. Our method also proves some special cases of the Forrester conjecture.Comment: 20 page

A family of q-Dyson style constant term identities

AbstractBy generalizing Gessel–Xin's Laurent series method for proving the Zeilberger–Bressoud q-Dyson Theorem, we establish a family of q-Dyson style constant term identities. These identities give explicit formulas for certain coefficients of the q-Dyson product, including three conjectures of Sills' as special cases and generalizing Stembridge's first layer formulas for characters of SL(n,C)

Ferroelastic switching with van der Waals direction transformation in layered PdSe2 driven by uniaxial and shear strain

Uniaxial and biaxial strain approaches are usually implemented to switch the ferroelastic states, which play a key role in the application of the ferroics and shape memory materials. In this work, by using the first-principles calculations, we found not only uniaxial strain, but also shear strain can induce a novel ferroelastic switching, in which the van der Waals (vdW) layered direction rotates with the ferroelastic transition in layered bulk PdSe2. The shear strain induces ferroelastic switching with three times amplitude smaller than uniaxial strain. The novel three-states ferroelastic switching in layered PdSe2 also occurs under shear strain. Our result shows that the shear strain could be used as an effective approach for manipulating the functionalities of layered materials in potential device applications