Geodesic
Constructing pseudo-involutions in the Riordan group
Journal of integer sequences, Tome 20 (2017) no. 4
Involutions and pseudo-involutions in the Riordan group are interesting because of their numerous applications. In this paper we study involutions using sequence characterizations of the Riordan arrays. For a given $B$-sequence we find the unique function $f(z)$ such that the array $(g(z), f (z))$ is a pseudo-involution. As a combinatorial application, we find the interpretation of each entry in the Bell array $(g(z),f(z))$ with a given $B$-sequence.
Classification : 05A15
Keywords: pseudo-involution, Riordan group, B-sequence, PI tree 
@article{JIS_2017__20_4_a4,
     author = {Phulara,  Dev and Shapiro,  Louis},
     title = {Constructing pseudo-involutions in the {Riordan} group},
     journal = {Journal of integer sequences},
     year = {2017},
     volume = {20},
     number = {4},
     zbl = {1357.05009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2017__20_4_a4/}
}
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Phulara,  Dev; Shapiro,  Louis. Constructing pseudo-involutions in the Riordan group. Journal of integer sequences, Tome 20 (2017) no. 4. http://geodesic.mathdoc.fr/item/JIS_2017__20_4_a4/