What does SA mean in UNCLASSIFIED

In this context, "SA" stands for "s" for Andrews. It is a notation used to represent the Andrews-Stanley symmetric function, which is a type of mathematical function that plays a role in the study of symmetric functions and combinatorics.

The Andrews-Stanley symmetric function is a fundamental symmetric function that has applications in various areas of mathematics, including combinatorics, representation theory, and algebraic geometry. It is named after George E. Andrews and Richard P. Stanley, who independently discovered it in the late 1970s.

The Andrews-Stanley symmetric function is defined as follows:

s_λ(x) = ∑_{σ∈S_n} (-1)^{inv(σ)} x^{σ(λ)}

where:

• λ is a partition of a non-negative integer n
• S_n is the symmetric group on n elements
• inv(σ) is the number of inversions in the permutation σ
• x is a set of variables

The Andrews-Stanley symmetric function has several important properties, including:

• It is a homogeneous symmetric function of degree n
• It is a Schur-positive function
• It has a generating function given by:

∑_{n=0}^\infty s_λ(x) t^n = \frac{1}{(1-tx_1)(1-tx_2) ... (1-tx_n)}

• It can be expressed in terms of other symmetric functions, such as the elementary symmetric functions and the power sum symmetric functions