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Enumeration of k-noncrossing trees and forests | ||
| Communications in Combinatorics and Optimization | ||
| دوره 7، شماره 2، اسفند 2022، صفحه 301-311 اصل مقاله (377.33 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2022.26903.1162 | ||
| نویسنده | ||
| Isaac Owino Okoth* | ||
| Department of Pure and Applied Mathematics, School of Mathematics, Statistics and Actuarial Science, Maseno University, Maseno, Kenya | ||
| چکیده | ||
| A $k$-noncrossing tree is a noncrossing tree where each node receives a label in $\{1,2,\ldots,k\}$ such that the sum of labels along an ascent does not exceed $k+1,$ if we consider a path from a fixed vertex called the root. In this paper, we provide a proof for a formula that counts the number of $k$-noncrossing trees in which the root (labelled by $k$) has degree $d$. We also find a formula for the number of forests in which each component is a $k$-noncrossing tree whose root is labelled by $k$. | ||
| کلیدواژهها | ||
| noncrossing trees؛ degree؛ forest | ||
| مراجع | ||
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