Geodesic
Combinatorial proofs of addition formulas
Xiang-Ke Chang ; Xing-Biao Hu1 ; Hongchuan Lei2 ; Yeong-Nan Yeh3
1LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences
2College of Science, Zhejiang Sci-Tech University
3Institute of Mathematics, Academia Sinica
The electronic journal of combinatorics, Tome 23 (2016) no. 1
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In this paper we give a combinatorial proof of an addition formula for weighted partial Motzkin paths. The addition formula allows us to determine the $LDU$ decomposition of a Hankel matrix of the polynomial sequence defined by weighted partial Motzkin paths. As a direct consequence, we get the determinant of the Hankel matrix of certain combinatorial sequences. In addition, we obtain an addition formula for weighted large Schröder paths.
DOI : 10.37236/4793
Classification : 05A19, 05A15, 15A15
Mots-clés : lattice paths, Catalan numbers, Motzkin numbers, large Schröder numbers, Hankel determinant

Xiang-Ke Chang    ; Xing-Biao Hu  1   ; Hongchuan Lei  2   ; Yeong-Nan Yeh  3

1 LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences
2 College of Science, Zhejiang Sci-Tech University
3 Institute of Mathematics, Academia Sinica 
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     author = {Xiang-Ke Chang and Xing-Biao Hu and Hongchuan Lei and Yeong-Nan Yeh},
     title = {Combinatorial proofs of addition formulas},
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     year = {2016},
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     number = {1},
     doi = {10.37236/4793},
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     url = {http://geodesic.mathdoc.fr/articles/10.37236/4793/}
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Xiang-Ke Chang; Xing-Biao Hu; Hongchuan Lei; Yeong-Nan Yeh. Combinatorial proofs of addition formulas. The electronic journal of combinatorics, Tome 23 (2016) no. 1. doi: 10.37236/4793

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