Combinatorial results for order-preserving partial injective contraction mappings

Let $I_n$ be the symmetric inverse semigroup on $X_n = \{1, 2, \ldots, n\}$. Let $OCI_n$ be the subsemigroup of $I_n$ consisting of all order-preserving injective partial contraction mappings, and let $ODCI_n$ be the subsemigroup of $I_n$ consisting of all order-preserving and order-decreasing injective partial contraction mappings of $X_n$. We investigate the cardinalities of some equivalences on $OCI_n$ and $ODCI_n$ which lead naturally to obtaining the order of these semigroups. Then, we relate the formulae obtained to Fibonacci numbers. Similar results about $ORCI_n$, the semigroup of order-preserving or order-reversing injective partial contraction mappings, are deduced.

Date and Venue

Start Date
Venue
Online Zoom meeting
End Date

Speaker

Georg Klein

Speaker's Institution

Universidade Federal da Bahia, Brasil

Files

Area

Semigroups, Automata and Languages

Financiamento