Firdous Ahmad Mala
1Department of Mathematics, Government Degree College Sopore, Baramulla, Jammu and Kashmir, India.
2Department of Mathematics, Chandigarh University, Gharuan Mohali, Punjab, India.
*Corresponding author: Firdous Ahmad Mala
Enumerative Combinatorics is the study of counting problems and counting techniques. Counting elements of various sets is a primary concern in Enumerative Combinatorics. An interesting observation about “counting problems” is the fact that they are somewhat easier to understand but hard to solve. This means that no specilaised or sophisticated knowledge is required to understand the subject-matter of Enumerative Combinatorics. However, an in-depth study of various counting techniques is often one of the several requirements for being able to solve these problems. Owing to this nature, this branch of mathematics has a plethora of open problems. Among them there are the problems of counting transitive relations, counting partial orders and counting quasiorders on a finite set. In this paper, we briefly revisit three closely-knit open problems in Enumerative Combinatorics. We also show how, in the light of the available literature, the solution of one of these three problems would lead to the solutions of the other two.
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