All Questions

Numerical semigroups are additive submonoids $A$ of the natural numbers such that the greatest common divisor of all elements of $A$ is 1. The complement of a numerical semigroup in $\mathbb{N}$ is ...

For any $m,k$ define $$ f_{m,k}(x_1,\ldots,x_n) = \sum_{1\le i_1<i_2<\cdots<i_m\le n} (x_{i_1}+\cdots+x_{i_m})^k. $$ Do these symmetric polynomials have a name and any theory?

Introduction: In the 1-dimensional case, given $m$-variables $$\mathbf{x} = (x_1,x_2,\dots,x_m)^T,$$ the elementary symmetric polynomials $(e_k(\mathbf{x}))_{k=1}^m$ give a "symmetric basis",...

I'm not familiar with the formalism of plethysm, so I need some help in unpacking the plethystic substitution $h_n[n\mathbf{z}]$ found in eqns. 5.6 and 5.9 of "Combinatorics of labelled ...

I've come across two matrix identities, flagged with daggers below, relating the two sets of elementary and complete homogeneous symmetric polynomials/functions via the two sets of refined Lah and ...