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Combinatorial proofs of addition formulas
Chang, Xiang-Ke1; Hu, Xing-Biao1; Lei, Hongchuan2; Yeh, Yeong-Nan3
2016-01-11
Source PublicationELECTRONIC JOURNAL OF COMBINATORICS
ISSN1077-8926
Volume23Issue:1Pages:13
AbstractIn 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 Schroder paths.
Keywordlattice paths Catalan numbers Motzkin numbers Large Schroder numbers Hankel determinant
Language英语
Funding ProjectNatural Science Foundation of Shandong Province of China[ZR2014AM001] ; NSC[104-2115-M-001-010-MY3]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000369985900008
PublisherELECTRONIC JOURNAL OF COMBINATORICS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/22074
Collection计算数学与科学工程计算研究所
Corresponding AuthorLei, Hongchuan
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing, Peoples R China
2.Zhejiang Sci Tech Univ, Coll Sci, Hangzhou, Zhejiang, Peoples R China
3.Acad Sinica, Inst Math, Taipei, Taiwan
Recommended Citation
GB/T 7714		 Chang, Xiang-Ke,Hu, Xing-Biao,Lei, Hongchuan,et al. Combinatorial proofs of addition formulas[J]. ELECTRONIC JOURNAL OF COMBINATORICS,2016,23(1):13.
APA Chang, Xiang-Ke,Hu, Xing-Biao,Lei, Hongchuan,&Yeh, Yeong-Nan.(2016).Combinatorial proofs of addition formulas.ELECTRONIC JOURNAL OF COMBINATORICS,23(1),13.
MLA Chang, Xiang-Ke,et al."Combinatorial proofs of addition formulas".ELECTRONIC JOURNAL OF COMBINATORICS 23.1(2016):13.
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