Mathematics Seminar - 10/15/25

Abstract:

Matroids arise as a unifying framework for independence in mathematics. In this talk, we will introduce matroids and then focus on the concept of loose and, more generally, k-loose elements: elements that only appear in "large" circuits. A matroid in which every element is loose is called paving, and it has been conjectured that almost every matroid is paving. We will present structural results on matroids over finite fields that contain loose or k-loose elements. These include sharp linear bounds on their size in terms of rank, partial characterizations when multiple loose elements occur, and strengthened results on paving matroids that extend earlier work.

Note:

Contact Prof. Shantia Yarahmadian at syarahmadian@math.msstate.edu or (662) 325-7143 for additional information.