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- W4383665188 abstract "We prove that the Catalan Lie idempotent $D_n(a,b)$, introduced in [Menous {it et al.}, Adv. Appl. Math. 51 (2013), 177] can be refined by introducing $n$ independent parameters $a_0,ldots,a_{n-1}$ and that the coefficient of each monomial is itself a Lie idempotent in the descent algebra. These new idempotents are multiplicity-free sums of subsets of the Poincar'e-Birkhoff-Witt basis of the Lie module. These results are obtained by embedding noncommutative symmetric functions into the dual noncommutative Connes-Kreimer algebra, which also allows us to interpret, and rederive in a simpler way, Chapoton's results on a two-parameter tree expanded series." @default.
- W4383665188 created "2023-07-09" @default.
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- W4383665188 date "2023-07-06" @default.
- W4383665188 modified "2023-09-25" @default.
- W4383665188 title "Tree expansions of some Lie idempotents}" @default.
- W4383665188 doi "https://doi.org/10.48550/arxiv.2307.03001" @default.
- W4383665188 hasPublicationYear "2023" @default.
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