We present two new algorithms for computing all Schur functions sκ(x1, . . . ,xn) for partitions κ such that |κ| ≤ N. Both algorithms have the property that for nonnegative arguments x1, . . . ,xn… (More)

In commutative algebra, a Weitzenböck derivation is a nonzero triangular linear derivation of the polynomial algebra K[x1, . . . , xm] in several variables over a field K of characteristic 0. The… (More)

Over a field of characteristic 0, the algebra of invariants of several n × n matrices under simultaneous conjugation by GLn is generated by traces of products of generic matrices. Teranishi, 1986,… (More)

This is an improved version of the talk of the author given at the Antalya Algebra Days VII on May 21, 2005. We present an introduction to the theory of the invariants under the action of GLn(C) by… (More)

We introduce the notion of Gröbner S-basis of an ideal of the free associative algebra K〈X〉 over a field K invariant under the action of a semigroup S of endomorphisms of the algebra. We calculate… (More)

We find explicitly the multiplicities in the (mixed) trace cochar-acter sequence of two 3 × 3 matrices over a field of characteristic 0 and show that asymptotically they behave as polynomials of… (More)

Recently Umirbaev has proved the long-standing Anick conjecture, that is, there exist wild automorphisms of the free associative algebra K〈x, y, z〉 over a field K of characteristic 0. In particular,… (More)

We consider absolutely free nonassociative algebras and, more generally, absolutely free algebras with (maybe infinitely) many multilinear operations. Such algebras are described in terms of labeled… (More)

The Bulgarian solitaire is a mathematical card game played by one person. A pack of n cards is divided into several decks (or “piles”). Each move consists of the removing of one card from each deck… (More)

Let F q [x, y] be the polynomial algebra in two variables over the finite field F q with q elements. We give an exact formula and the asymptotics for the number p n of automorphisms (f, g) of F q [x,… (More)