Gordon and McMahon defined a two-variable greedoid polynomial f(G; t, z) for any greedoid G. They studied greedoid polynomials for greedoids associated with rooted graphs and rooted digraphs. They proved that greedoid polynomials of rooted digraphs have the multiplicative direct sum property. In addition, these polynomials are divisible by \(1 + z\) under certain conditions. We compute the greedoid polynomials for all rooted digraphs up to order six. A polynomial is said to factorise if it has a non-constant factor of lower degree. We study the factorability of greedoid polynomials of rooted digraphs, particularly those that are not divisible by \(1 + z\). We give some examples and an infinite family of rooted digraphs that are not direct sums but their greedoid polynomials factorise.

Gordon 和 McMahon为任何贪心G定义了一个二变量贪心多项式f ( G ;  t ,  z ) 。他们研究了与有根图和有根有向图相关的贪心多项式。他们证明了有根有向图的贪婪多项式具有乘法直接和的性质。此外，这些多项式在某些条件下可以被\(1 + z\)整除。我们为所有有根有向图计算高达六阶的贪婪多项式。如果多项式具有较低阶的非常数因子，则称其为因式分解。我们研究有根有向图的贪婪多项式的可分解性，特别是那些不能被\(1 + z\)。我们给出了一些例子和一个无限的有根有向图族，它们不是直接和，而是它们的贪婪多项式因式分解。