Abstract
Let (Formula presented.) For a partial one–one transformation (or subpermutation) (Formula presented.) of (Formula presented.) the following parameters are defined: the height (Formula presented.) , the waist (Formula presented.) , and the fix (Formula presented.). We compute the cardinalities of some equivalence classes defined by equalities of these parameters on (Formula presented.) and (Formula presented.) the semigroups of order-preserving and of order-preserving or order-reversing subpermutations of (Formula presented.) respectively. As a consequence, we obtain several formulae and generating functions for the number of nilpotents in (Formula presented.) and (Formula presented.). We also prove that, for large (Formula presented.) a randomly chosen order-preserving (resp. order-reversing) subpermutation of (Formula presented.) has probability (Formula presented.) (resp. (Formula presented.) ) of being nilpotent.
| Original language | English |
|---|---|
| Pages (from-to) | 269-283 |
| Number of pages | 15 |
| Journal | Journal of Difference Equations and Applications |
| Volume | 21 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - Mar 4 2015 |
| Externally published | Yes |
Keywords
- asymptotic behaviour
- generating function
- nilpotent transformation
- order-preserving and order-reversing subpermutations
- recurrence relation
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory
- Applied Mathematics