Riordan group approaches in matrix factorizations
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Abstract:
In this paper, we consider an arbitrary binary polynomial sequence {A_n} and then give a lower triangular matrix representation of this sequence. As main result, we obtain a factorization of the innite generalized Pascal matrix in terms of this new matrix, using a Riordan group approach. Further some interesting results and applications are derived.
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riordan group approaches in matrix factorizations
in this paper, we consider an arbitrary binary polynomial sequence {a_n} and then give a lower triangular matrix representation of this sequence. as main result, we obtain a factorization of the in nite generalized pascal matrix in terms of this new matrix, using a riordan group approach. further some interesting results and applications are derived.
full textThe Double Riordan Group
The Riordan group is a group of infinite lower triangular matrices that are defined by two generating functions, g and f . The kth column of the matrix has the generating function gfk. In the Double Riordan group there are two generating function f1 and f2 such that the columns, starting at the left, have generating functions using f1 and f2 alternately. Examples include Dyck paths with level s...
full textThe Riordan group
Shapiro, L.W., S. Getu, W.-J. Woan and L.C. Woodson, The Riordan group, Discrete Applied Mathematics 34 (1991) 229-239.
full textMatrix Characterizations of Riordan Arrays
Here we discuss two matrix characterizations of Riordan arrays, P -matrix characterization and A-matrix characterization. P -matrix is an extension of the Stieltjes matrix defined in [25] and the production matrix defined in [7]. By modifying the marked succession rule introduced in [18], a combinatorial interpretation of the P -matrix is given. The P -matrix characterizations of some subgroups...
full textThe Sheffer group and the Riordan group
We define the Sheffer group of all Sheffer-type polynomials and prove the isomorphism between the Sheffer group and the Riordan group. An equivalence of the Riordan array pair and generalized Stirling number pair is also presented. Finally, we discuss a higher dimensional extension of Riordan array pairs. AMS Subject Classification: 05A15, 11B73, 11B83, 13F25, 41A58
full textLearning with matrix factorizations
Matrices that can be factored into a product of two simpler matrices can serve as a useful and often natural model in the analysis of tabulated or highdimensional data. Models based on matrix factorization (Factor Analysis, PCA) have been extensively used in statistical analysis and machine learning for over a century, with many new formulations and models suggested in recent years (Latent Sema...
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Journal title
volume 38 issue 2
pages 491- 506
publication date 2012-07-15
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