We study relation between two interpretations of the Tutte polynomial of a matroid perspective $M_1\to M_2$ on a set E given with a linear ordering <. A well known interpretation uses internal and external activities on a family $\mathcal{B}(M_1,M_2)$ of the sets independent in $M_1$ and spanning in $M_2$. Recently we introduced another interpretation based on a family $\mathcal{D}(M_1,M_2;<)$ of “cyclic bases” of $M_1\to M_2$ with respect to <. We introduce a one-to-one correspondence between $\mathcal{B}(M_1,M_2)$ and $\mathcal{D}(M_1,M_2;<)$ that also generates a relation between the interpretations of the Tutte polynomial of a matroid perspective and corresponds with duality.

中文翻译：

---

图特多项式的解释之间一一对应

我们研究拟阵视角的 Tutte 多项式的两种解释之间的关系${米}_{\mathrm{1个}}\to {米}_{\mathrm{2个}}$在以线性顺序 < 给出的集合E上。一个众所周知的解释使用家庭的内部和外部活动$\mathcal{乙}({米}_{\mathrm{1个}},{米}_{\mathrm{2个}})$独立于${米}_{\mathrm{1个}}$并跨越${米}_{\mathrm{2个}}$. 最近我们介绍了另一种基于家庭的解释$\mathcal{丁}({米}_{\mathrm{1个}},{米}_{\mathrm{2个}};<)$的“循环碱基”${米}_{\mathrm{1个}}\to {米}_{\mathrm{2个}}$关于 <. 我们引入了一对一的对应关系$\mathcal{乙}({米}_{\mathrm{1个}},{米}_{\mathrm{2个}})$和$\mathcal{丁}({米}_{\mathrm{1个}},{米}_{\mathrm{2个}};<)$这也会在拟阵透视图的 Tutte 多项式的解释之间产生一种关系，并与对偶性相对应。