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Séminaire Lotharingien de Combinatoire, 78B.10 (2017), 12 pp.

# Hugh Thomas and Nathan Williams

# Sweeping up Zeta

**Abstract.**
We repurpose the main theorem of [Thomas and Williams, 2014] to prove
that modular sweep maps are bijective. We conclude that the general
sweep maps defined in [Armstrong, Loehr, and Warrington, 2014] are
bijective. As a special case of particular interest, this gives the
first proof that the zeta map on rational Dyck paths is a bijection.

Received: November 14, 2016.
Accepted: February 17, 2017.
Final version: April 1, 2017.

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