#### Title

### Non-Decreasing Sequences

#### Faculty Sponsor

Jon Beagley

#### College

Arts and Sciences

#### Department/Program

Mathematics and Statistics/MSEED

#### Presentation Type

Poster Presentation

#### Symposium Date

Summer 7-31-2017

#### Abstract

Non-decreasing sequences are a generalization of binary covering arrays, which has made research on non-decreasing sequences important in both math and computer science. A non-decreasing sequence of subsets of a finite set S of size *s, *{S_{1}, S_{2},.... S_{t}}, 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 subsequent 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 for 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*.

#### Recommended Citation

Klass, Amy E. and Bruno, Alexander, "Non-Decreasing Sequences" (2017). *Summer Interdisciplinary Research Symposium*. 3.

https://scholar.valpo.edu/sires/3