Lattice Paths and Order-preserving Partial Transformations

2013/04/29 by A. Laradji, Laradji, A., A. Umar +1 · 1 citation
Mathematics · #05A10 #05A15 #20M18 #20M20 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A10 #msc:05A15 #msc:20M18 #msc:20M20

paper · pdf · doi:10.48550/arxiv.1304.7574

18 pages, 6 figures

arxiv created 2013/04/29 · arxiv updated 2013/04/30

Abstract

Let \cal PO_n be the semigroup of all order-preserving partial transformations of a finite chain. It is shown that there exist bijections between the set of certain lattice paths in the Cartesian plane that start at (0,0), end at (n-1,n-1), and certain subsemigroups of \cal PO_n. Several consequences of these bijections were discussed.

Cited by

• On the small Schröder semigroup SS^′_n

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