论文标题
组合订单的部分注射式收缩映射
Combinatorial results for order-preserving partial injective contraction mappings
论文作者
论文摘要
令$ \ MATHCAL {i} _n $为$ x_n = \ {1，2，\ ldots，n \} $的对称反向半群。令$ \ MATHCAL {OCI} _n $为$ \ MATHCAL {i} _n $由所有订购的订单保护的部分置换映射组成的子集团，让$ \ natercal {odci} _n $成为$ \ natercal的订单和订单的订单和所有订单的中等序列。 $ x_n $的注入性部分收缩映射。在本文中，我们研究了$ \ Mathcal {oci} _n $和$ \ Mathcal {odci} _n $自然而然地获得这些半群的顺序的$ \ Mathcal {oci} _n $和$ \ Mathcal {odci} _n $的基础。然后，我们将获得的公式与斐波那契数相关联。推导了有关$ \ Mathcal {orci} _n $的类似结果，该_n $是订单保存或订购订单的半群的注入性部分收缩映射。
Let $ \mathcal{I}_n$ be the symmetric inverse semigroup on $X_n = \{1, 2, \ldots , n\}$. Let $\mathcal{OCI}_n$ be the subsemigroup of $\mathcal{I}_n$ consisting of all order-preserving injective partial contraction mappings, and let $\mathcal{ODCI}_n$ be the subsemigroup of $\mathcal{I}_n$ consisting of all order-preserving and order-decreasing injective partial contraction mappings of $X_n$. In this paper, we investigate the cardinalities of some equivalences on $\mathcal{OCI}_n$ and $\mathcal{ODCI}_n$ which lead naturally to obtaining the order of these semigroups. Then, we relate the formulae obtained to Fibonacci numbers. Similar results about $\mathcal{ORCI}_n$, the semigroup of order-preserving or order-reversing injective partial contraction mappings, are deduced.
