Results of computer assisted research are presented. The subject of research are properties of posets related to sorting by comparisons.

In the first part of the thesis the gold partition conjecture (GPC) is stated. It is proved that the GPC implies the well known 1/3-2/3 Conjecture and a tight upper bound for the minimal number of comparisons always sufficient to sort a poset. The GPC is proved for posets of width two, semiorders and posets containing sufficiently many of minimal or maximal elements. It is also proved that the fraction of partial orders on an n-element set satisfying the GPC converges to 1 when n approaches infinity. The GPC is verified, using computer, for all posets containing at most 11 elements. Computer assisted proof of the GPC for 6-thin posets is presented.

In the second part of the thesis results of computer search for the most unbalanced posets are presented. Observed regularity leads us to define a new class of badly balanced posets, which are called ladders with broken rungs.

In the third part of the thesis there are presented algorithms, which can be used to verify if a given poset can be sorted using a given number of comparisons. These algorithms are used to compute the minimal number of comparisons always sufficient to sort 14 and 15 elements. They are also used to prove that n = 47 is the minimal number of elements for which there exists an algorithm such that: m and n - m elements are sorted using the Ford-Johnson algorithm first, then the sorted sequences are merged and the total number of used comparisons is smaller than the number of comparisons used by the Ford-Johnson algorithm to sort n elements directly. The minimal numbers of comparisons always sufficient to merge m and n - m elements for all 2m <= n <= 23 are also computed.