Abstract
In this paper, we establish a bijection between standard domino tableaux with at most three rows and partial Motzkin paths. Moreover, we establish a connection between skew standard domino tableaux with at most three rows and a variant of partial Motzkin paths within the nonnegative quadrant and enumerate such tableaux with n dominoes in terms of linear combinations of Motzkin numbers.
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References
Aigner M.: Motzkin numbers. European J. Combin. 19(6), 663–675 (1998)
Barbasch D., Vogan D.: Primitive ideals and orbital integrals in complex classical groups. Math. Ann. 259(2), 153–199 (1982)
Bonnafé, C., Geck, M., Iancu, L., Lam, T.: On domino insertion and Kazhdan-Lusztig cells in type B n . In: Gyoja, A., Nakajima, H., Shinoda, K.-i., Shoji, T., Tanisaki, T. (eds.) Representation Theory of Algebraic Groups and Quantum Groups, pp. 33–54. Birkhäuser, Boston (2010)
Chen W.Y.C., Li N.Y., Shapiro L.W., Yan S.H.F.: Matrix identities on weighted partial Motzkin paths. European J. Combin. 28(4), 1196–1207 (2007)
Egge E.S.: Enumerating rc-invariant permutations with no long decreasing subsequences. Ann. Combin. 14(1), 85–101 (2010)
Eu S.-P.: Skew-standard tableaux with three rows. Adv. Appl. Math. 45(4), 463–469 (2010)
Eu S.-P., Fu T.-S., Hou J.T., Hsu T.-W.: Standard Young tableaux and colored Motzkin paths. J. Combin. Theory Ser. A 120(7), 1786–1803 (2013)
van Leeuwen, M.A.A.: Some bijective correspondences involving domino tableaux. Electronic J. Combin. 7, #R35 (2000)
Kim, J.H.: On the enumeration of three-rowed standard Young tableaux of skew shapes in terms of Motzkin numbers. arXiv:1107.3873 (2011)
Niederhausen, H.: Inverses of Motzkin and Schröder paths. Integers 12, #A49 (2012)
The OEIS Foundation Inc., The On-Line Encyclopedia of Integer Sequences. Published electronically at http://oeis.org
Trapa P.E.: Symplectic and orthogonal Robinson-Schensted algorithms. J. Algebra 286(2), 386–404 (2005)
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Cheng, TY., Eu, SP., Fu, TS. et al. Skew Standard Domino Tableaux and Partial Motzkin Paths. Ann. Comb. 21, 43–71 (2017). https://doi.org/10.1007/s00026-017-0340-6
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DOI: https://doi.org/10.1007/s00026-017-0340-6