Generally, B,,(x) is a polynomial of exact degree n, although degeneracies can occur. For
example, iff itself is a polynomial of degree m, then 5,(f: s) is also of degree tn for all n> m …

Operator-Theoretic Positivstellensätze Page 1 Zeitschrift für Analysis und ihre Anwendungen
Journal for Analysis and its Applications Volume 22 (2003), No. 2, 299–314 Operator-Theoretic …

Poisson brackets on the polynomial algebra C [x, y, z] are studied. A description of all such
brackets is given and, for a significant class of Poisson brackets, the Poisson prime ideals …

An Introduction to Quasisymmetric Schur Functions is aimed at researchers and graduate
students in algebraic combinatorics. The goal of this monograph is twofold. The first goal is …

We show that the Grothendieck bialgebra of the semi-tower of partition lattice algebras is
isomorphic to the graded dual of the bialgebra of symmetric functions in noncommutative …

The multiplication algebra of a bernstein algebra: basic results Page 1 COMMUNICATIONS IN
ALGEBRA, 24(5), 1809- 182 1 (1 996) THE MULTIPLICATION ALGEBRA OF A BERNSTEIN …

We give a representation of the classical theory of multiplicative arithmetic functions (MF) in
the ring of symmetric polynomials written on the isobaric basis. The representing elements …

Let f1,..., fpbe polynomials in n variables with coefficients in a fieldK. We associate with these
polynomials a number of functional equations and related ideals B, Bjand BΣ ofK [s1,..., sp] …

Noncommutative symmetric functions have many properties analogous to those of classical
(commutative) symmetric functions. For instance, ribbon Schur functions (analogs of the …

Let NSymm be the Hopf algebra of non-commutative symmetric functions (in an infinity of
indeterminates): NSymm= Z. It is shown that an associative algebra A with a Hasse-Schmidt …