论文信息 - Humps for Dyck and for Motzkin paths

Humps for Dyck and for Motzkin paths

We calculate the total number of humps in Dyck and in Motzkin paths, and we give Standard-Young-Tableaux-interpretations of the numbers involved. One then observes the intriguing phenomena that the humps-calculations change the partitions in a strip to partitions in a hook.

A. Regev

[1] Dominique Gouyou-Beauchamps,et al. Standard Young Tableaux of Height 4 and 5 , 1989, Eur. J. Comb..

[2] I. G. MacDonald,et al. Symmetric functions and Hall polynomials , 1979 .

[3] Sen-Peng Eu. On the three-rowed skew standard Young tableaux , 2010, 1002.4060.

[4] Amitai Regev,et al. Asymptotic values for degrees associated with strips of young diagrams , 1981 .

[5] Amitai Regev,et al. Hook young diagrams with applications to combinatorics and to representations of Lie superalgebras , 1987 .

[6] Amitai Regev,et al. Probabilities in the (k, ℓ) hook , 2009 .

[7] N. J. A. Sloane,et al. The On-Line Encyclopedia of Integer Sequences , 2003, Electron. J. Comb..

[8] Saulo Alves de Araujo,et al. Identification of novel keloid biomarkers through Profiling of Tissue Biopsies versus Cell Cultures in Keloid Margin specimens Compared to adjacent Normal Skin , 2010, Eplasty.

[9] Doron Zeilberger,et al. The Method of Creative Telescoping , 1991, J. Symb. Comput..

[10] Charalambos A. Charalambides,et al. Enumerative combinatorics , 2018, SIGA.