Combinatorial Proofs of Addition Formulas

[摘要] 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 pa

[学科分类] 离散数学和组合数学

[关键词] Lattice paths;Catalan numbers;Motzkin numbers;Large Schr\"{o}der numbers;Hankel determinant