TY - JOUR
T1 - Combinatorial results for semigroups of order-preserving or order-reversing subpermutations
AU - Laradji, A.
AU - Umar, A.
N1 - Publisher Copyright:
© 2015 Taylor & Francis.
PY - 2015/3/4
Y1 - 2015/3/4
N2 - 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.
AB - 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.
KW - asymptotic behaviour
KW - generating function
KW - nilpotent transformation
KW - order-preserving and order-reversing subpermutations
KW - recurrence relation
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U2 - 10.1080/10236198.2015.1005080
DO - 10.1080/10236198.2015.1005080
M3 - Article
AN - SCOPUS:84924337176
SN - 1023-6198
VL - 21
SP - 269
EP - 283
JO - Journal of Difference Equations and Applications
JF - Journal of Difference Equations and Applications
IS - 3
ER -