Fantastic Patterns and Where Not to Find Them

Authors

Michael Bukata, Valparaiso UniversityFollow
Ryan Kulwicki, Valparaiso UniversityFollow
Nicholas Lewandowski, Valparaiso UniversityFollow
Lara Pudwell, Valparaiso UniversityFollow
Jacob Roth, Valparaiso UniversityFollow
Teresa Wheeland, Valparaiso UniversityFollow

Faculty Sponsor

Lara Pudwell

College

Arts and Sciences

Discipline(s)

Mathematics and Statistics

Presentation Type

Poster Presentation

Symposium Date

Spring 5-3-2018

Abstract

Interesting patterns are everywhere we look, but what happens when we try to avoid patterns? A permutation is a list of numbers in a specific order. When we avoid a pattern, we try not to order those numbers in certain ways. For example, the permutation 45312 avoids the 123 pattern because no three elements in the permutation are in an increasing order. In our work, we studied the permutations that avoid two different patterns of length three. We focused on the distribution of peaks, valleys, double ascents, and double descents over these sets of permutations.

Biographical Information about Author(s)

Teresa Wheeland is a sophomore math and secondary education major, Nicholas Lewandowski is a sophomore math and secondary education major, Ryan Kulwicki is a junior math and computer science major, Jacob Roth is a sophomore math and computer science major, and Michael Bukata is a sophomore math major.

Recommended Citation

Bukata, Michael; Kulwicki, Ryan; Lewandowski, Nicholas; Pudwell, Lara; Roth, Jacob; and Wheeland, Teresa, "Fantastic Patterns and Where Not to Find Them" (2018). Symposium on Undergraduate Research and Creative Expression (SOURCE). 744.
https://scholar.valpo.edu/cus/744