Abstract
Let In be the symmetric inverse semigroup on Xn = {1, 2, . . ., n}. Let OCIn be the subsemigroup of In consisting of all order-preserving injective partial contraction mappings, and let ODCIn be the subsemigroup of In consisting of all order-preserving and order-decreasing injective partial contraction mappings of Xn. In this paper, we investigate the cardinalities of some equivalences on OCIn and ODCIn which lead naturally to obtaining the order of these semigroups. Then, we relate the formulae obtained to Fibonacci numbers. Similar results about ORCIn, the semigroup of order-preserving or order-reversing injective partial contraction mappings, are deduced.
| Original language | British English |
|---|---|
| Pages (from-to) | 1-19 |
| Number of pages | 19 |
| Journal | Contributions to Discrete Mathematics |
| Volume | 19 |
| Issue number | 2 |
| State | Published - 2024 |
Keywords
- fix of a transformation; Fibonacci number
- right (left) shoulder
- semigroups of transformations; partial injective contraction mappings; right (left) waist