Riordan group involutions and the Δ-sequence

Authors:
Gi-Sang Cheon;Sung-Tae Jin;Hana Kim;Louis W. Shapiro
Affiliations:
Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea;Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea;Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea;Department of Mathematics, Howard University, Washington, DC 20059, USA
Venue:
Discrete Applied Mathematics
Year:
2009

Citing 4
Cited 1

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Note: Self-inverse Sheffer sequences and Riordan involutions

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Abstract

Several important combinatorial arrays, after inserting some minus signs, turn out to be involutions when considered as lower triangular matrices. Among these are the Pascal, RNA, and directed animal matrices. These examples and many others are in the Bell subgroup of the Riordan group. We characterize all such pseudo-involutions by means of a single sequence called the @D-sequence. Finally we compute the @D-sequences for the powers of a pseudo-involution in the Bell subgroup.