Dedekind Number - Summation Formula

Summation Formula

Kisielewicz (1988) rewrote the logical definition of antichains into the following arithmetic formula for the Dedekind numbers:

where is the th bit of the number, what can be written using the floor function as

However, this formula is not helpful for computing the values of M(n) for large n due to the large number of terms in the summation.

Read more about this topic:  Dedekind Number

Famous quotes containing the words summation and/or formula:

    He maintained that the case was lost or won by the time the final juror had been sworn in; his summation was set in his mind before the first witness was called. It was all in the orchestration, he claimed: in knowing how and where to pitch each and every particular argument; who to intimidate; who to trust, who to flatter and court; who to challenge; when to underplay and exactly when to let out all the stops.
    Dorothy Uhnak (b. 1933)

    Ideals possess the strange quality that if they were completely realized they would turn into nonsense. One could easily follow a commandment such as “Thou shalt not kill” to the point of dying of starvation; and I might establish the formula that for the proper functioning of the mesh of our ideals, as in the case of a strainer, the holes are just as important as the mesh.
    Robert Musil (1880–1942)