Euler-Catalan's number triangle and its application
Статья в журнале
In this paper, we study such combinatorial objects as labeled binary trees of size n with m ascents on the left branch and labeled Dyck n-paths with m ascents on return steps. For these combinatorial objects, we present the relation of the generated number triangle to Catalan's and Euler's triangles. On the basis of properties of Catalan's and Euler's triangles, we obtain an explicit formula that counts the total number of such combinatorial objects and a bivariate generating function. Combining the properties of these two number triangles allows us to obtain different combinatorial objects that may have a symmetry, for example, in their form or in their formulas.
Журнал:
- Symmetry
- MDPI (Basel)
- Индексируется в Scopus, Web of Science
Библиографическая запись: Shablya, Y. V. Euler-Catalan's number triangle and its application / Y. V. Shablya, D. V. Kruchinin // Symmetry. - 2020. - Vol. 12. - Iss. 4. - P 600. - DOI: 10.3390/SYM12040600
Ключевые слова:
NUMBER TRIANGLE LABELED BINARY TREE LABELED DYCK PATH EULER–CATALAN’S TRIANGLE GENERATING FUNCTIONИндексируется в:
- Web of science ( https://apps.webofknowledge.com/full_record.do?product=WOS&search_mode=GeneralSearch&qid=5&SID=F1kUtVEclELfeoeOm6t&page=1&doc=1 )
- Scopus ( https://www.scopus.com/record/display.uri?eid=2-s2.0-85087063997&origin=inward )