M. Morin

math.CO2010

Differences of Augmented Staircase Skew Schur Functions

Matthew Morin

We define a fat staircase to be a Ferrers diagram corresponding to a partition of the form $(n^{α_{n}}, n - 1^{α_{n - 1}}, ..., 1^{α_{1}})$ , where $α = (α_{1}, ..., α_{n})$ is a composition, or…

math.CO2010

Skew Schur Functions of Sums of Fat Staircases

Matthew Morin

We define a fat staircase to be a Ferrers diagram corresponding to a partition of the form $(n^{α_{n}}, n - 1^{α_{n - 1}}, ..., 1^{α_{1}})$ , where $α = (α_{1}, ..., α_{n})$ is a composition, or…

math.CO2010

Differences of Skew Schur Functions of Staircases with Transposed Foundations

Matthew Morin

We consider the skew diagram $Δ_{n}$ , which is the $18 0^{\circ}$ rotation of the staircase diagram $δ_{n} = (n, n - 1, n - 2, ..., 2, 1)$ . We create a staircase with bad foundation by augmenting…

math.CO2006

On distinguishing trees by their chromatic symmetric functions

Jeremy L. Martin, Matthew Morin, Jennifer D. Wagner

Let $T$ be an unrooted tree. The \emph{chromatic symmetric function} $X_{T}$ , introduced by Stanley, is a sum of monomial symmetric functions corresponding to proper colorings of $T$ …