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General numeration I. Gauged schemes.

D. W. Dubois (1982)

Revista Matemática Hispanoamericana

The paper deals with special partitions of whole numbers in the following form: given a sequence of pairs {[Gi;Di]} of positive integers in which the Gi form a strictly increasing sequence, sums of the form ∑niGi, with 0 ≤ ni ≤ Di, are considered. The correspondence[nk ... n0] → ∑i≤k niGidefines then a mapping α from a set M of numerals, called Neugebauer symbols, satisfying 0 ≤ ni ≤ Di, into the set W of all non-negative integers. In M, initial zeros are supressed and M is ordered in the usual...

Generalized poly-Cauchy polynomials and their interpolating functions

Takao Komatsu, Florian Luca, Claudio de J. Pita Ruiz V. (2014)

Colloquium Mathematicae

We give a generalization of poly-Cauchy polynomials and investigate their arithmetical and combinatorial properties. We also study the zeta functions which interpolate the generalized poly-Cauchy polynomials.

Generalized Schröder matrices arising from enumeration of lattice paths

Lin Yang, Sheng-Liang Yang, Tian-Xiao He (2020)

Czechoslovak Mathematical Journal

We introduce a new family of generalized Schröder matrices from the Riordan arrays which are obtained by counting of the weighted lattice paths with steps E = ( 1 , 0 ) , D = ( 1 , 1 ) , N = ( 0 , 1 ) , and D ' = ( 1 , 2 ) and not going above the line y = x . We also consider the half of the generalized Delannoy matrix which is derived from the enumeration of these lattice paths with no restrictions. Correlations between these matrices are considered. By way of illustration, we give several examples of Riordan arrays of combinatorial interest. In addition,...

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