Symmetric Functions, Formal Group Laws, and Lazard's Theorem

Symmetric Functions, Formal Group Laws, and Lazard's Theorem

Lazard's theorem is a central result in formal group theory; it states that the ring over which the universal formal group law is deened (known as the Lazard ring) is a polynomial algebra over the integers with innnitely many generators. This ring also shows up in algebraic topology as the complex cobordism ring. The main aim of this paper is to show that the polynomial structure of the Lazard ...

Quantum Cobordisms and Formal Group Laws

We would like to congratulate Israel Moiseevich Gelfand on the occasion of his 90th birthday and to thank the organizers P. Etingof, V. Retakh and I. Singer for the opportunity to take part in the celebration. The present paper is closely based on the lecture given by the second author at The Unity of Mathematics Symposium and is based on our joint work in progress on Gromov–Witten invariants w...

Noncommutative Vieta Theorem and Symmetric Functions

There are two ways to generalize basic constructions of commutative algebra for a noncommutative case. More traditional way is to define commutative functions like trace or determinant over noncommuting variables. Beginning with [6] this approach was widely used by different authors, see for example [5], [15], [14], [12], [11], [7]. However, there is another possibility to work with purely nonc...

Counting rotation symmetric functions using Polya's theorem

Homogeneous rotation symmetric (invariant under cyclic permutation of the variables) Boolean functions have been extensively studied in recent years due to their applications in cryptography. In this paper we give an explicit formula for the number of homogeneous rotation symmetric functions over the finite field GF(pm) using Polya’s enumeration theorem, which completely solves the open problem...

The symmetric group - representations, combinatorial algorithms, and symmetric functions