Non-decreasing Sequences

Abstract. Non-decreasing sequences are a generalization of binary covering arrays, which has made re- search on non-decreasing sequences important in both math and computer science. A non-decreasing se- quence of subsets of a finite set S of size s, {S1, S2, . . . , St}, length t, and strength d, is a sequence of non-empty subsets where the union of any d previous subsets in the sequence does not contain any subse- quent subset. The goal of this research is to find properties of these non-decreasing sequences as the variables d, s, and t change. We also explored methods of creating a maximum length for a non-decreasing sequence given d and s. Through our research, we discovered and proved basic properties of these non-decreasing sequences. In addition to this, we can describe a method we used while trying to find the maximum length of a sequence. In the future, research can be conducted to find an exact formula that will generate a maximum length sequence given a non-decreasing sequence of strength d