A note on connectivity preserving splitting operation for matroids representable over $GF(p)$

Abstract

In general, element splitting operation on a matroid M with ground set E is the operation defined by creating a single element coextension of M by adding an element x that creates a cocircuit with T ⊂ E which is not a cocircuit of M . And then deletion of x from this coextension gives a T -split of M denoted by MT . Note that T -split of M may not preserve the n-connectivity of the matroid M . The present paper defines related notion of element splitting operation for matroids representable over GF (p) which preserves the n-connectivity of the matroid and characterizes circuits, bases and hyperplanes of the resulting matroid. The effect of this operation on Eulerian, bipartite and connected matroids which are representable over GF (p) is also studied.