Year: 2023
Type: preprint
Abstract: We show that the problem of counting the number of $n$-variable unate functions reduces to the problem of counting the number of $n$-variable monotone functions. Using recently obtained results on $n$-variable monotone functions, we obtain counts of $n$-variable unate functions up to $n=9$. We use an enumeration strategy to obtain the number of $n$-variable balanced monotone functions up to $n=7$. We show that the problem of counting the number of $n$-variable balanced unate functions reduces to the problem of counting the number of $n$-variable balanced monotone functions, and consequently, we obtain the number of $n$-variable balanced unate functions up to $n=7$. Using enumeration, we obtain the numbers of equivalence classes of $n$-variable balanced monotone functions, unate functions and balanced unate functions up to $n=6$. Further, for each of the considered sub-class of $n$-variable monotone and unate functions, we also obtain the corresponding numbers of $n$-variable non-degenerate functions.
Source: arXiv (Cornell University)
Authors: Biswas, Aniruddha, Sarkar, Palash
Institution: Indian Statistical Institute
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4367365804