Fuss-Catalan algebras and their one- and two-boundary versions are realized on increasing chains of non-crossing partitions, with a new r=2 reflection equation solution.
Path representation of maximal parabolic Kazhdan-Lusztig polynomials
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We provide simple rules for the computation of Kazhdan--Lusztig polynomials in the maximal parabolic case. They are obtained by filling regions delimited by paths with "Dyck strips" obeying certain rules. We compare our results with those of Lascoux and Sch\"utzenberger.
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Fuss--Catalan algebras on generalized Dyck paths via non-crossing partitions
Fuss-Catalan algebras and their one- and two-boundary versions are realized on increasing chains of non-crossing partitions, with a new r=2 reflection equation solution.