Statistical Aspects of Two Classes of Random Binomial Trees and Forests
We consider two specific families of binomial trees and forests: simply generated binomial <i>d</i>-ary trees and forests versus their increasing phylogenetic version, with tree nodes in increasing order from the root to any of its leaves. The analysis (both pre-asymptotic and asymptotic...
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MDPI AG
2025-01-01
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| Series: | Mathematics |
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| author | Thierry E. Huillet |
| author_facet | Thierry E. Huillet |
| author_sort | Thierry E. Huillet |
| collection | DOAJ |
| description | We consider two specific families of binomial trees and forests: simply generated binomial <i>d</i>-ary trees and forests versus their increasing phylogenetic version, with tree nodes in increasing order from the root to any of its leaves. The analysis (both pre-asymptotic and asymptotic) consists of some of the main statistical features of their total progenies. We take advantage of the fact that the random distribution of those trees are obtained while weighting the counts of the underlying combinatorial trees. We finally briefly stress a rich alternative randomization of combinatorial trees and forests, based on the ratio of favorable count outcomes to the total number of possible ones. |
| format | Article |
| id | doaj-art-28720053304f40e0b7794b3475b66b4b |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-28720053304f40e0b7794b3475b66b4b2025-01-24T13:40:03ZengMDPI AGMathematics2227-73902025-01-0113229110.3390/math13020291Statistical Aspects of Two Classes of Random Binomial Trees and ForestsThierry E. Huillet0Laboratoire de Physique Théorique et Modélisation (CNRS, UMR 8089), CY Cergy Paris Université, 95302 Cergy-Pontoise, FranceWe consider two specific families of binomial trees and forests: simply generated binomial <i>d</i>-ary trees and forests versus their increasing phylogenetic version, with tree nodes in increasing order from the root to any of its leaves. The analysis (both pre-asymptotic and asymptotic) consists of some of the main statistical features of their total progenies. We take advantage of the fact that the random distribution of those trees are obtained while weighting the counts of the underlying combinatorial trees. We finally briefly stress a rich alternative randomization of combinatorial trees and forests, based on the ratio of favorable count outcomes to the total number of possible ones.https://www.mdpi.com/2227-7390/13/2/291simply generated and increasing binomial trees and foreststotal progenygenerating functionsLagrange inversion formulastructural statisticspartition structures |
| spellingShingle | Thierry E. Huillet Statistical Aspects of Two Classes of Random Binomial Trees and Forests Mathematics simply generated and increasing binomial trees and forests total progeny generating functions Lagrange inversion formula structural statistics partition structures |
| title | Statistical Aspects of Two Classes of Random Binomial Trees and Forests |
| title_full | Statistical Aspects of Two Classes of Random Binomial Trees and Forests |
| title_fullStr | Statistical Aspects of Two Classes of Random Binomial Trees and Forests |
| title_full_unstemmed | Statistical Aspects of Two Classes of Random Binomial Trees and Forests |
| title_short | Statistical Aspects of Two Classes of Random Binomial Trees and Forests |
| title_sort | statistical aspects of two classes of random binomial trees and forests |
| topic | simply generated and increasing binomial trees and forests total progeny generating functions Lagrange inversion formula structural statistics partition structures |
| url | https://www.mdpi.com/2227-7390/13/2/291 |
| work_keys_str_mv | AT thierryehuillet statisticalaspectsoftwoclassesofrandombinomialtreesandforests |