2 citations · 5 across the 5 of their papers we have counts for
6 papers
Congruences for Dedekind numbers
Bartłomiej Pawelski, Andrzej Szepietowski, Błażej Szepietowski
We study congruence properties of Dedekind numbers . Our approach relies on actions of -subgroups of symmetric groups on posets of monotone functions and leads to the congr…
Counting interval sizes in the poset of monotone Boolean functions
Bartłomiej Pawelski
We focus on the computational aspects of counting interval sizes in the poset , which represents all monotone Boolean functions of variables. We present a resource-aware a…
Counting self-dual monotone Boolean functions
Bartłomiej Pawelski, Andrzej Szepietowski
Let denote the set of monotone Boolean functions with variables. Elements of can be represented as strings of bits of length . Two elements of are repres…
On the number of inequivalent monotone Boolean functions of 9 variables
Bartłomiej Pawelski
We provide the first-ever calculation of the number of inequivalent monotone Boolean functions of 9 variables, which is equal to 789,204,635,842,035,040,527,740,846,300,252,680.
Divisibility properties of Dedekind numbers
Bartlomiej Pawelski, Andrzej Szepietowski
We study some divisibility properties of Dedekind numbers. We show that the ninth Dedekind number is congruent to 6 modulo 210.
On the number of inequivalent monotone Boolean functions of 8 variables
Bartłomiej Pawelski
In this paper, the author presents algorithms that allow determining the number of fixed points in permutations of a set of monotone Boolean functions. Then, using Burnside's lemma…