Product expansions

Product Jacobi Expansions 3

Combinatorial Analysis of Integer Power Product Expansions

Let f (x) = 1+ ∑n=1 anx n be a formal power series with complex coefficients. Let {rn}n=1 be a sequence of nonzero integers. The Integer Power Product Expansion of f (x), denoted ZPPE, is ∏k=1(1+wkx k)rk . Integer Power Product Expansions enumerate partitions of multi-sets. The coefficients {wk}k=1 themselves possess interesting algebraic structure. This algebraic structure provides a lower bou...

Quantum Inequalities from Operator Product Expansions

Quantum inequalities are lower bounds for local averages of quantum observables that have positive classical counterparts, such as the energy density or the Wick square. We establish such inequalities in general (possibly interacting) quantum field theories on Minkowski space, using nonperturbative techniques. Our main tool is a rigorous version of the operator product expansion.

Expansions , Free Inverse Semigroups , and Schiitzenberger Product

In this paper we shall present a new constructron of the free inverse monoid on a set A’. Contrary to the prevrous constructions of 19, 111, our construction is symmetric and originates from classrcal ideas of language theory. The mgredlents of this construction are the free group on X and the relatron that associates to a word II’ of the free monoid on X, the set of all pairs (u, v) such that ...

On Series Expansions of Capparelli’s Infinite Product

Using Lie theory, Stefano Capparelli conjectured an interesting Rogers-Ramanujan type partition identity in his 1988 Rutgers Ph.D. thesis. The first proof was given by George Andrews, using combinatorial methods. Later, Capparelli was able to provide a Lie theoretic proof. Most combinatorial Rogers-Ramanujan type identities (e.g. the Göllnitz-Gordon identities, Gordon’s combinatorial generaliza...