A CHARACTERIZATION OF THE RIORDAN BELL SUBGROUP BY C-SEQUENCES

  • Jin, Sung-Tae (Department of Mathematics, Sungkyunkwan University)
  • Received : 2009.03.09
  • Published : 20090600

Abstract

In this paper, we consider a new sequence called by the C-sequence of the Riordan array. It allows us to find a simple proof for several combinatorial identities. Further, we prove that a C-sequence characterizes Bell subgroup of the Riordan group.

Keywords

References

  1. G.-S. Cheon, H. Kim and L. W. Shapiro, Riordan group involutions, Lin. Alg. Appl., 428 (2008), 941-952. https://doi.org/10.1016/j.laa.2007.09.003
  2. D. G. Rogers, Pascal triangles, Catalan numbers and renewal arrays, Discrete Math. 22 (1978), 301-310. https://doi.org/10.1016/0012-365X(78)90063-8
  3. L. W. Shapiro, Bijections and the Riordan group, Theoretical Computer Science, 307 (2003), 403-413. https://doi.org/10.1016/S0304-3975(03)00227-5
  4. L. W. Shapiro, S. Getu, W.-J. Woan and L. Woodson, The Riordan group, Discrete Appl. Math. 34 (1991), 229-239. https://doi.org/10.1016/0166-218X(91)90088-E