Abstract
Let POn be the semigroup of order-preserving partial transformations on an n-chain. We establish several results for the number F(n,m) of elements of POn with m fixed points, including recurrence relations and generating functions. We also prove that the probability that, for large n, a randomly chosen map in POn has exactly m fixed points is asymptotically 22(2m + 1)/n.
| Original language | English |
|---|---|
| Article number | 2250082 |
| Journal | Journal of Algebra and its Applications |
| Volume | 21 |
| Issue number | 4 |
| DOIs | |
| State | Published - 1 Apr 2022 |
Bibliographical note
Publisher Copyright:© 2022 World Scientific Publishing Company.
Keywords
- Order-preserving transformation
- asymptotic behavior
- fixed points
- generating function
- nilpotent transformation
- recurrence relation
ASJC Scopus subject areas
- Algebra and Number Theory
- Applied Mathematics
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