A Baxter class of a different kind, and other bijective results using tableau sequences ending with a row shape
Discrete mathematics & theoretical computer science, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) (2015)
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Tableau sequences of bounded height have been central to the analysis of $k$-noncrossing set partitions and matchings. We show here that families of sequences that end with a row shape are particularly compelling and lead to some interesting connections. First, we prove that hesitating tableaux of height at most two ending with a row shape are counted by Baxter numbers. This permits us to define three new Baxter classes which, remarkably, do not obviously possess the antipodal symmetry of other known Baxter classes. Oscillating tableau of height bounded by $k$ ending in a row are in bijection with Young tableaux of bounded height 2$k$. We discuss this recent result, and somegenerating function implications. Many of our proofs are analytic in nature, so there are intriguing combinatorial bijections to be found.
@article{DMTCS_2015_special_285_a74,
author = {Burrill, Sophie and Melczer, Stephen and Mishna, Marni},
title = {A {Baxter} class of a different kind, and other bijective results using tableau sequences ending with a row shape},
journal = {Discrete mathematics & theoretical computer science},
year = {2015},
volume = {DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)},
doi = {10.46298/dmtcs.2530},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2530/}
}
TY - JOUR AU - Burrill, Sophie AU - Melczer, Stephen AU - Mishna, Marni TI - A Baxter class of a different kind, and other bijective results using tableau sequences ending with a row shape JO - Discrete mathematics & theoretical computer science PY - 2015 VL - DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) UR - http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2530/ DO - 10.46298/dmtcs.2530 LA - en ID - DMTCS_2015_special_285_a74 ER -
%0 Journal Article %A Burrill, Sophie %A Melczer, Stephen %A Mishna, Marni %T A Baxter class of a different kind, and other bijective results using tableau sequences ending with a row shape %J Discrete mathematics & theoretical computer science %D 2015 %V DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) %U http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2530/ %R 10.46298/dmtcs.2530 %G en %F DMTCS_2015_special_285_a74
Burrill, Sophie; Melczer, Stephen; Mishna, Marni. A Baxter class of a different kind, and other bijective results using tableau sequences ending with a row shape. Discrete mathematics & theoretical computer science, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) (2015). doi: 10.46298/dmtcs.2530
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