Séminaire Lotharingien de Combinatoire, 80B.33 (2018), 12 pp.
Baptiste Louf
A New Family of Bijections for Planar Maps
Abstract.
We present bijections for the planar cases of two formulas on
maps that arise from the KP hierarchy (Goulden-Jackson and
Carrell-Chapuy formulas), relying on a "cut-and-slide" operation.
This is the first time a bijective proof is given for quadratic map-counting formulas derived from the KP hierarchy. Up to now, only the linear one-faced case was known (Harer-Zagier recurrence and Chapuy-Féray-Fusy bijection).
As far as we know, this bijection is new and not equivalent to any of the well-known bijections between planar maps and tree-like objects.
Received: November 14, 2017.
Accepted: February 17, 2018.
Final version: April 1, 2018.
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