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Tableau sequences of bounded height have been central to the analysis ofk-noncrossing set partitions and matchings. We show here that familes ofsequences that end with a row shape are particularly compelling and lead tosome interesting connections. First, we prove that hesitating tableaux ofheight at most two ending with a row shape are counted by Baxter numbers. Thispermits us to define three new Baxter classes which, remarkably, do notobviously possess the antipodal symmetry of other known Baxter classes. We thenconjecture that oscillating tableau of height bounded by k ending in a row arein bijection with Young tableaux of bounded height 2k. We prove this conjecturefor k at most eight by a generating function analysis. Many of our proofs areanalytic in nature, so there are intriguing combinatorial bijections to befound.

A Baxter class of a different kind, and other bijective results using tableau sequences ending with a row shape