Crystal graphs are powerful combinatorial tools for working with the plactic monoid and symmetric functions. Quasi-crystal graphs are an analogous concept for the hypoplactic monoid and quasi-symmetric functions. We explicitly describe a previously observed isomorphism of components of the quasi-crystal graph, introducing a new combinatorial structure called quasi-array. As an application, we explore the interaction of fundamental quasi-symmetric functions and Schur functions, and the arrangement of quasi-crystal components within crystal components.
This is joint work with Alan Cain, António Malheiro and Fátima Rodrigues.
|