Skew Standard Domino Tableaux and Partial Motzkin Paths

被引：1

作者：

Cheng, Ting-Yuan ^{[1
]}

Eu, Sen-Peng ^{[2
]}

Fu, Tung-Shan ^{[3
]}

Lee, Yi-Lin ^{[4
]}

机构：

[1] Natl Taiwan Univ, Dept Comp Sci & Informat Engn, Taipei 10617, Taiwan

[2] Chinese Air Force Acad, Kaohsiung 82047, Taiwan

[3] Natl Pingtung Univ, Dept Appl Math, Pingtung 90003, Taiwan

[4] Natl Cent Univ, Dept Math, Taoyuan 32001, Taiwan

来源：

ANNALS OF COMBINATORICS | 2017年 / 21卷 / 01期

关键词：

standard domino tableaux; skew standard domino tableaux; Motzkin paths; partial Motzkin paths;

D O I：

10.1007/s00026-017-0340-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：43 / 71

页数：29

共 12 条

[1] Motzkin numbers [J].

Aigner, M .

EUROPEAN JOURNAL OF COMBINATORICS, 1998, 19 (06) :663-675

[2] PRIMITIVE-IDEALS AND ORBITAL INTEGRALS IN COMPLEX CLASSICAL-GROUPS [J].

BARBASCH, D ;

VOGAN, D .

MATHEMATISCHE ANNALEN, 1982, 259 (02) :153-199

[3] On Domino Insertion and Kazhdan-Lusztig Cells in Type Bn [J].

Bonnafe, Cedric ;

Geck, Meinolf ;

Iancu, Lacrimioara ;

Lam, Thomas .

REPRESENTATION THEORY OF ALGEBRAIC GROUPS AND QUANTUM GROUPS, 2010, 284 :33-+

[4] Matrix identities on weighted partial Motzkin paths [J].

Chen, William Y. C. ;

Li, Nelson Y. ;

Shapiro, Louis W. ;

Yan, Sherry H. F. .

EUROPEAN JOURNAL OF COMBINATORICS, 2007, 28 (04) :1196-1207

[5] Enumerating rc-Invariant Permutations with No Long Decreasing Subsequences [J].

Egge, Eric S. .

ANNALS OF COMBINATORICS, 2010, 14 (01) :85-101

[6] Standard Young tableaux and colored Motzkin paths [J].

Eu, Sen-Peng ;

Fu, Tung-Shan ;

Hou, Justin T. ;

Hsu, Te-Wei .

JOURNAL OF COMBINATORIAL THEORY SERIES A, 2013, 120 (07) :1786-1803

[7] Skew-standard tableaux with three rows [J].

Eu, Sen-Peng .

ADVANCES IN APPLIED MATHEMATICS, 2010, 45 (04) :463-469

[8]

Kim J. H., 2011, ARXIV11073873

[9]

Niederhausen H., 2012, INTEGERS, V12

[10]

The OEIS Foundation Inc, ON LINE ENCY INTEGER

← 1 2 →