论文标题
配对函数无周期的彩色环
Grothendieck ring of the pairing function without cycles
论文作者
论文摘要
$ m^2 $和$ m $之间的双重$（l，r）$据说是一个配对功能，没有循环，如果其坐标函数的任何组成没有固定点。我们在这里计算配对函数的Grothendieck戒指，没有周期为$ \ Mathbb {z}^2 \ simeq \ Mathbb {z} [x]/（x-x^2）$。更一般而言，对于任何$ n \ in \ mathbb {n}^*$，以及在没有循环的任何生物jetion中，$ m $和$ m^n $，完全相同的方法证明了$ k_0（m）= \ mathbb {z}} [x]/（x-x^n）$。
A bijection $(l,r)$ between $M^2$ and $M$ is said to be a pairing function with no cycles, if any composition of its coordinate functions has no fixed point. We compute here the Grothendieck ring of the pairing function without cycles to be isomorphic to $\mathbb{Z}^2\simeq \mathbb{Z}[X]/(X-X^2)$. More generally, for any $n\in \mathbb{N}^*$ and any bijetion without cycles betwen $M$ and $M^n$, the exact same method proves that $K_0(M)=\mathbb{Z}[X]/(X-X^n)$.
