3 papers
math.CO2026
Partition division maps, symmetric functions and positivity
Per Alexandersson, Lilan Dai
We study a linear map on symmetric functions that ``divides'' a partition by a positive integer , sending a Schur function indexed by a partition of to a symmetric function…
math.CO2025
Symmetric statistics on rational Dyck paths
Lilan Dai, Shishuo Fu, Dun Qiu
Rational Dyck paths are the rational generalization of classical Dyck paths. They play an important role in Catalan combinatorics, and have multiple applications in algebra and geo…
math.RA2022
Primitive decompositions of idempotents of the group algebras of dihedral groups and generalized quaternion groups
Lilan Dai, Yunnan Li
In this paper, we introduce a method computing the primitive decomposition of idempotents of any semisimple finite group algebra based on its matrix representations and Wedderburn…