Combinatorial proofs of addition formulas

Xiang-Ke Chang Xing-Biao Hu Hongchuan Lei Yeong-Nan Yeh

Dynamical Systems mathscidoc:1912.43174

the electronic journal of combinatorics, 23, (1), 1-8, 2016.1
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 Schrder paths.
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  title={Combinatorial proofs of addition formulas},
  author={Xiang-Ke Chang, Xing-Biao Hu, Hongchuan Lei, and Yeong-Nan Yeh},
  booktitle={the electronic journal of combinatorics},
Xiang-Ke Chang, Xing-Biao Hu, Hongchuan Lei, and Yeong-Nan Yeh. Combinatorial proofs of addition formulas. 2016. Vol. 23. In the electronic journal of combinatorics. pp.1-8.
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