A372495 Number of inequivalent unate functions of n or fewer variables.

2, 4, 10, 34, 200, 3466, 829744

Offset: 0

Author

Aniruddha Biswas, May 03 2024

Keywords

• nonn
• hard
• more

Comments

A Boolean function is unate in a variable if it is either nondecreasing or nonincreasing with respect to that variable. Therefore in the circuit representation of unate functions, each variable appears either in its original form or in complemented form. Thus x⊕y = (x∧¬y)∨(¬x∧y) is not a unate function.

Moreover, two Boolean functions are said to be equivalent if they are equivalent under the permutation of variables. For example, f(x,y)=x is equivalent to f(x,y)=y under the permutation of input variables.

Examples

			The list of all 2-variable inequivalent unate functions f(x,y) is 0,1,x,¬x,x∧y,¬x∧y,¬x∧¬y,x∨y,¬x∨y,¬x∨¬y. So a(2)=10.
		

Links

• Aniruddha Biswas and Palash Sarkar, Counting unate and balanced monotone Boolean functions, arXiv:2304.14069 [math.CO], 2023.
• Aniruddha Biswas and Palash Sarkar, Counting Unate and Monotone Boolean Functions Under Restrictions of Balancedness and Non-Degeneracy, J. Int. Seq. (2025) Vol. 28, Art. No. 25.3.4. See pp. 4, 16.
• Index entries for sequences related to Boolean functions

Crossrefs

Cf. A000372, A003182, A245079.