We define a new family F̃w(X) of generating functions for w ∈ S̃n which are affine analogues of Stanley symmetric functions. We establish basic properties of these functions including symmetry, dominance and conjugation. We conjecture certain positivity properties in terms of a subfamily of symmetric functions called affine Schur functions. As applications, we show how affine Stanley symmetric fu...

Stanley has studied a symmetric function generalization XG of the chromatic polynomial of a graph G. The innocent-looking Stanley-Stembridge Poset Chain Conjecture states that the expansion of XG in terms of elementary symmetric functions has nonnegative coefficients if G is a clawfree incomparability graph. Here we give a combinatorial interpretation of these coefficients by combining Gasharov...

The efficacy of chlorine and hot water treatments in killing Salmonella stanley inoculated onto alfalfa seeds was determined. Treatment of seeds containing 10(2) to 10(3) CFU/g in 100-micrograms/ml active chlorine solution for 5 or 10 min caused a significant (P < or = 0.05) reduction in population, and treatment in 290-micrograms/ml chlorine solution resulted in a significant reduction compare...

An algorithm is given to compute a Stanley decomposition for the normal form of a three degree of freedom Hamiltonian at equilibrium in the semisimple resonant case. This algorithm is then applied to compute Stanley decompositions of the normal form of the first and second order resonances.

Given a simplicial complex, it is easy to construct a generic deformation of its Stanley-Reisner ideal. The main question under investigation in this paper is how to characterize the simplicial complexes such that their Stanley-Reisner ideals have Cohen-Macaulay generic deformations. Algorithms are presented to construct such deformations for matroid complexes, shifted complexes, and tree compl...