In recent years, much work has been devoted to a systematic study of polynomial identities certifying strict or non-strict positivity of a polynomial f on a basic closed set K ⊂ R. The interest in such identities originates not least from their importance in polynomial optimization. The majority of the important results requires the archimedean condition, which implies that K has to be compact....

We give the formula for multiplying a Schubert class on an odd orthogonal or symplectic flag manifold by a special Schubert class pulled back from the Grassmannian of maximal isotropic subspaces. This is also the formula for multiplying a type B (respectively, type C) Schubert polynomial by the Schur P -polynomial pm (respectively, the Schur Q-polynomial qm). Geometric constructions and interme...

In a previous paper we investigated the (exponential) bipartitional polynomials involving polynomial sequences of trinomial type. Our aim is to give properties of bipartitional polynomials related to the derivatives of polynomial sequences of trinomial type. Furthermore, we deduce identities involving Bell polynomials.

In recent years, much work has been devoted to a systematic study of polynomial identities certifying strict or non-strict positivity of a polynomial f on a basic closed set K ⊂ R. The interest in such identities originates not least from their importance in polynomial optimization. The majority of the important results requires the archimedean condition, which implies that K has to be compact....

Motivated by the fundamental lower bounds questions in proof complexity, we investigate the complexity of generating identities of matrix rings, and related problems. Specifically, for a field F let A be a non-commutative (associative) F-algebra (e.g., the algebra Matd(F) of d × d matrices over F). We say that a non-commutative polynomial f(x1, . . . , xn) over F is an identity of A, if for all...

We use computer algebra to determine all the multilinear polynomial identities of degree ≤ 7 satisfied by the trilinear operations (a · b) · c and a · (b · c) in the free dendriform dialgebra, where a · b is the pre-Lie or the pre-Jordan product. For the pre-Lie triple products, we obtain one identity in degree 3, and three independent identities in degree 5, and we show that every identity in ...