TY - JOUR
T1 - Combinatorial results for semigroups of orientation-preserving partial transformations
AU - Umar, A.
PY - 2011
Y1 - 2011
N2 - Let Xn = {1, 2,..., n}. On a partial transformation α: Dom α ⊆ Xn! Im α ⊆ Xn of Xn the following parameters are defined: the breadth or width of α is {pipe} Dom α {pipe}, the height of α is {pipe} Im α {pipe}, and the right (resp., left) waist of α is max(Im α) (resp., min(Im α)). We compute the cardinalities of some equivalences defined by equalities of these parameters on OPn, the semigroup of orientation-preserving full transformations of Xn, POPn the semigroup of orientation-preserving partial transformations of Xn, ORn the semigroup of orientation-preserving/reversing full transformations of Xn, and PORn the semigroup of orientation-preserving/reversing partial transformations of Xn, and their partial one-to-one analogue semigroups, POPIn and PORIn.
AB - Let Xn = {1, 2,..., n}. On a partial transformation α: Dom α ⊆ Xn! Im α ⊆ Xn of Xn the following parameters are defined: the breadth or width of α is {pipe} Dom α {pipe}, the height of α is {pipe} Im α {pipe}, and the right (resp., left) waist of α is max(Im α) (resp., min(Im α)). We compute the cardinalities of some equivalences defined by equalities of these parameters on OPn, the semigroup of orientation-preserving full transformations of Xn, POPn the semigroup of orientation-preserving partial transformations of Xn, ORn the semigroup of orientation-preserving/reversing full transformations of Xn, and PORn the semigroup of orientation-preserving/reversing partial transformations of Xn, and their partial one-to-one analogue semigroups, POPIn and PORIn.
KW - Anti-cyclic sequence
KW - Breadth
KW - Cyclic sequence
KW - Full transformation
KW - Height
KW - Left waist
KW - Orientation-preserving transformation
KW - Orientation-reversing transformation
KW - Partial one-to-one transformation
KW - Partial transformation
KW - Right waist
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M3 - Article
AN - SCOPUS:80053068522
SN - 1530-7638
VL - 14
JO - Journal of Integer Sequences
JF - Journal of Integer Sequences
IS - 7
ER -