This Is AuburnElectronic Theses and Dissertations

Existence of TP(d,k,n)




Aliyev, Natig

Type of Degree

PhD Dissertation


Mathematics and Statistics


Given a square grid of land, which has n rows and n columns. It is required to plant trees on the land so that there are k trees in every row and column and there is at most 1 tree in any small square part of the land with d rows and d columns. What should be the values of n, k and d? How to plant the trees? The objective of this dissertation is to analyze the problem and come up with the answers to the questions proposed above. The dissertation consists of two main parts. The first part provides necessary and sufficient conditions regarding the values of n, k and d. The second part of the dissertation delivers the method to plant the trees on the land under given constraints.