Résumé : Baxter numbers are a well known number sequence enumerating Baxter permutations and several other combinatorial objects. In this talk, we define a new class of objects called Slicings of parallelogram polyominoes counted by Baxter numbers that enables us to find a continuum from Catalan structures to Baxter structures. This continuum is established by means of a new succession rule (i.e. generating tree) associated with Schröder numbers, that interpolates between the known succession rules for Baxter and Catalan numbers. Then, similarly we consider a generalization for the Baxter succession rule that forms a link between Baxter numbers and Factorial numbers. Such succession rule defines semi-Baxter numbers, which result to count plane permutations, whose enumeration was set as an open problem by Bousquet-Mélou and Butler, and inversion sequences avoiding (210,100), as conjectured by Martinez and Savage.
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