Year: 2026
Type: article
Abstract: This paper unifies disparate areas of combinatorics. Namely, graph theory and integer partition theory. A partition of an integer n is a finite sequence $$a_1, a_2, \ldots , a_j$$ a 1 , a 2 , … , a j of weakly increasing positive integers (called parts) whose sum is n . In order to achieve a unification, a specific type of graph called a c-graph is defined for each partition. The main thrust of the paper is investigating the degrees of vertices in c-graphs. For each of the possible fixed degrees $$i \in \{1,2,3,4\}$$ i ∈ { 1 , 2 , 3 , 4 } , we find generating functions in which the coefficient of $$x^n y^j$$ x n y j is the number of vertices of degree i in all c-graphs with n vertices and j parts.
Source: The Ramanujan Journal
Authors: Aubrey Blecher, Arnold Knopfmacher
Institution: University of the Witwatersrand
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
OpenAlex ID: W7224835675