论文标题
在Malvenuto-Reutenauer Hopf代数的无取消反码公式上
On the cancellation-free antipode formula for the Malvenuto-Reutenauer Hopf Algebra
论文作者
论文摘要
对于Malvenuto-Reutenauer Hopf代数，我们为任何形式的$ ab1 \ cdots（b-1）（b+1）\ cdots（a+1）（a+1）\ cdots n $的置换提供了无取消的反模型公式，该公式始于减少序列$ ab $ $ ab $ $ ab $ $ ab $ ab $ ab $ ab $ ab $ ab $ $ 1 \ CDOTS（B-1）（B+1）\ CDOTS（A-1）（A+1）\ CDOTS N $，其中$ 1 \ leq B <a \ leq n $。结果，我们证实了卡罗来纳州贝内德蒂和布鲁斯·E·萨根（Bruce E. Sagan）提出的两个猜想。
For the Malvenuto-Reutenauer Hopf algebra of permutations, we provide a cancellation-free antipode formula for any permutation of the form $ab1\cdots(b-1)(b+1)\cdots(a-1)(a+1)\cdots n$, which starts with the decreasing sequence $ab$ and ends with the increasing sequence $1\cdots(b-1)(b+1)\cdots(a-1)(a+1)\cdots n$, where $1\leq b<a\leq n$. As a consequence, we confirm two conjectures posed by Carolina Benedetti and Bruce E. Sagan.
