Christian Smith

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math.CO2020

Up- and Down-Operators on Young's Lattice

Ricky Ini Liu, Christian Smith

The up-operators $u_{i}$ and down-operators $d_{i}$ (introduced as Schur operators by Fomin) act on partitions by adding/removing a box to/from the $i$ th column if possible. It is well…

math.CO2019

The Algebra of Schur Operators

Ricky Ini Liu, Christian Smith

We study a representation of the (local) plactic monoid given by Schur operators $u_{i}$ , which act on partitions by adding a box in column $i$ (if possible). In particular, we give…