https://repository.maseno.ac.ke/handle/123456789/92 2026-05-15T12:09:31Z 2026-05-15T12:09:31Z Kariuki, Yvonne Wakuthii Okoth, Isaac Owino Nyamwala, Fredrick Oluoch https://repository.maseno.ac.ke/handle/123456789/6225 2024-11-12T16:00:56Z 2024-07-02T00:00:00Z

Counting formulas and bijections of nondecreasing 2-noncrossing trees Kariuki, Yvonne Wakuthii; Okoth, Isaac Owino; Nyamwala, Fredrick Oluoch In this paper, we introduce nondecreasing 2-noncrossing trees and enumerate them according to their number of vertices, root degree, and number of forests. We also introduce nondecreasing 2-noncrossing increasing trees and count them by considering their number of vertices, label of the root, label of the leftmost child of the root, root degree, and forests. We observe that the formulas enumerating the newly introduced trees are generalizations of little and large Schroder ¨ numbers. Furthermore, we establish bijections between the sets of nondecreasing 2-noncrossing trees, locally oriented noncrossing trees, labelled complete ternary trees, and 3-Schroder paths.

2024-07-02T00:00:00Z Nyariaro, Albert Oloo Okoth, Isaac Owino https://repository.maseno.ac.ke/handle/123456789/6224 2024-11-12T15:55:03Z 2024-08-18T00:00:00Z

Enumeration of k-plane trees and forests Nyariaro, Albert Oloo; Okoth, Isaac Owino A k-plane tree is an ordered tree in which the vertices are labelled by integers {1, 2, . . . , k} and satisfies the condition i + j ⩽ k + 1 where i and j are adjacent vertices in the tree. These trees are known to be counted by Fuss-Catalan numbers. In this paper, we use generating functions and decomposition of trees to enumerate these trees according to degree of the root, label of the first child of the root and number of forests of k-plane trees. The results of this paper generalize known results for 2-plane trees and plane trees.

2024-08-18T00:00:00Z Gideon Kasivu, Jonathan Mwania, Josphert Kimatu, Leonard Kamau, Janet Mulwa, Redempta Kiilu, Rose Kithungu, Mr James Musyoka, Rebecca Migwambo https://repository.maseno.ac.ke/handle/123456789/6153 2024-08-11T07:51:42Z 2024-04-05T00:00:00Z

Reinforcing the 21st century pedagogical skills through the application of the question formulation technique (QFT) in secondary schools in south eastern region of Kenya Gideon Kasivu, Jonathan Mwania, Josphert Kimatu, Leonard Kamau, Janet Mulwa, Redempta Kiilu, Rose Kithungu, Mr James Musyoka, Rebecca Migwambo Studies show that only 27% of graduates believe that Universities and colleges taught them how to ask their own questions. The Question Formulation Technique (QFT) imparts students a way that makes them to think critically every time they read, connect the concepts and when deciding whether to take facts and information at face value or to dig a little deeper. Generally, it is reported that students ask less than a fifth of the questions teachers estimated would be elicited and deemed desirable Poor participation by students in the questioning during teaching and learning process has often led to poor learning outcomes which are manifested by poor performance in academics. The study was instituted to evaluate the equipping of 21st skills to secondary schools’ students using QFT trained teachers in ten schools in the South Eastern Region of Kenya. The teachers and students were trained to develop skills in producing of questions, categorizing questions, prioritizing questions and in reflections. The study found that teachers were eager to be trained in QFT skills so as to enhance an observed low student engagement and poor performance. The assessment of the implementation of QFT in content delivery found that students had many questions to ask if given opportunity and not judged during the teaching and learning process. The analysis of the questions showed that the QFT sparked student’s potentials into divergent, convergent and metacognition types of thinking during and after the teaching and learning process. The teachers had a challenge of focusing the student class questions to achieve the lesson objectives in the stipulated time of the lesson. However, online engagement of students with teacher was observed to be a key in spurring more learners’ curiosity in learning and in developing patterns in their thinking and ask questions and facilitate lifelong learning. https://dx.doi.org/10.47772/IJRISS.2024.803060

2024-04-05T00:00:00Z Kariuki, Yvonne Wakuthii Okoth, Isaac Owino Nyamwala, Fredrick Oluoch https://repository.maseno.ac.ke/handle/123456789/6146 2024-08-07T13:07:58Z 2024-08-08T00:00:00Z

On non-decreasing 2-plane trees Kariuki, Yvonne Wakuthii; Okoth, Isaac Owino; Nyamwala, Fredrick Oluoch In this paper, we have introduced the set of non-decreasing 2-plane trees. These are plane trees whose vertices receive labels from the set {1, 2} such that the sum of labels of adjacent vertices is at most 3 and that the labels of siblings are weakly increasing from left to right. We have obtained the formula for the number of these trees with a given number of vertices and label of the root. Further, we have obtained the number of these trees given root degrees and label of the eldest child of the root. We have also constructed bijections between the set of non-decreasing 2-plane trees with roots labelled 2 and the sets of little Schröder paths, plane trees in which leaves receive two labels, restricted lattice paths and increasing tableaux. For non-decreasing 2-plane trees with roots labelled 1, we have obtained bijections between the set of these trees and the sets of large Schröder paths and row-increasing tableaux.

2024-08-08T00:00:00Z Nyariaro, Albert Oloo Okoth, Isaac Owino https://repository.maseno.ac.ke/handle/123456789/6145 2024-08-07T12:58:38Z 2024-09-01T00:00:00Z

Bijections for classes of labelled trees. Nyariaro, Albert Oloo; Okoth, Isaac Owino Trees are acyclic connected graphs. Plane trees, d-ary trees, binary trees, noncrossing trees and their generalizations, which are families of trees, have been enumerated by many authors using various statistics. These trees are known to be enumerated by Catalan or Catalan-like formulas (Fuss-Catalan numbers). One of the most common approaches to the enumeration of these trees is by means of generating functions. Another method that can be used to enumerate them is by constructing bijections between sets of the same cardinality. The bijective method is preferred to other methods by many combinatorialists. So, in this paper, we construct bijections relating k-plane trees, k-noncrossing increasing trees, k-noncrossing trees, k-binary trees and weakly labelled k-trees.

2024-09-01T00:00:00Z Oburu, Jeffar Were, Joshua Oduor, Brian Nyakinda, Joseph https://repository.maseno.ac.ke/handle/123456789/6083 2024-04-29T15:02:53Z 2023-12-01T00:00:00Z

On (P, Q)-Binomial Extension of Cox-Ross-Rubinstein Model in Skorohod Spaces. Oburu, Jeffar; Were, Joshua; Oduor, Brian; Nyakinda, Joseph In this paper, we develope a (pq)-binomial extension of the Cox-Ross-Rubinstein (CRR) model thereby enhancing its ap plicability in optimizing life insurance portfolios amidst noisy observations. We utilize mathematical constructs designed to mitigate the impact of nancial perturbations, thereby enrich ing the existing model and laying a robust foundation for nav igating uncertainties.

2023-12-01T00:00:00Z Were, Joshua Oduor, Brian Nyakinda, Joseph https://repository.maseno.ac.ke/handle/123456789/6082 2024-04-29T14:56:42Z 2024-03-11T00:00:00Z

Portfolio optimization for extended (p, q) –binomial cox –ross- rubinstein model Were, Joshua; Oduor, Brian; Nyakinda, Joseph In this paper, we focus on establishing optimization conditions for the extended binomial Cox-Ross-Rubinstein (CRR)model, particularly in the context of managing portfolios in life insurance under varying noise conditions. We also give the convergence analysis of the model. Journal homepage: https://ssarpublishers.com/ssarjms/

2024-03-11T00:00:00Z Mawora, Thomas Otieno, Joyce Vance, Eric. A https://repository.maseno.ac.ke/handle/123456789/6080 2024-04-23T18:12:35Z 2022-06-07T00:00:00Z

Exploring the Need for a Statistical Collaboration Laboratory in a Kenyan University: Experiences, Challenges, and Opportunities Mawora, Thomas; Otieno, Joyce; Vance, Eric. A This paper explores the need for a statistical collaboration laboratory or “stat lab”(Vance and Pruitt 2022) at Maseno University in Kenya. It describes the experiences, challenges, and opportunities for statistics lecturers who established a statistical collaboration laboratory or “stat lab” called the Maseno University Laboratory for Interdisciplinary Statistical Analysis

2022-06-07T00:00:00Z Kariuki, Yvonne Wakuthii https://repository.maseno.ac.ke/handle/123456789/6061 2024-03-25T13:11:13Z 2023-10-19T00:00:00Z

Bijections of plane Husimi graphs and certain combinatorial structures Kariuki, Yvonne Wakuthii Plane Husimi graphs are combinatorial structures obtained when we replace edges in plane trees with complete graphs such that the resultant structures are connected and cycle free. The formula that counts these structures is known to enumerate other combinatorial structures. In this paper, we construct bijections between the set of plane Husimi graphs and the sets of plane trees, dissections of convex polygons, sequences satisfying certain properties, standard Young tableaux, Deutsch paths and restricted lattice paths. http://ejma.euap.org

2023-10-19T00:00:00Z Nyariaro, Albert P. Oloo Okoth, Isaac .Owino https://repository.maseno.ac.ke/handle/123456789/6060 2024-03-25T12:54:26Z 2024-01-09T00:00:00Z

Bijections for classes of labelled trees Nyariaro, Albert P. Oloo; Okoth, Isaac .Owino Trees are acyclic connected graphs. Plane trees, d-ary trees, binary trees, non crossing trees and their generalizations, which are families of trees, have been enumerated by many authors using various statistics. These trees are known to be enumerated by Catalan or Catalan-like formulas (Fuss-Catalan numbers). One of the most common approaches to the enumeration of these trees is by means of generating functions. Another method that can be used to enumerate them is by constructing bijections between sets of the same cardinality. The bijective method is preferred to other methods by many combinatorialists. So, in this paper, we construct bijections relating k-plane trees, k-noncrossing increasing trees, k-noncrossing trees, k-binary trees and weakly labelled k-trees.

2024-01-09T00:00:00Z