INTERPRETATIONS OF ELEMENTS OF TWO INTERPOLATION CLASSES OF INTEGER SEQUENCES

Author(s): Bondarenko L.N.

Rubric: Methodological research

DOI: 10.21777/2500-2112-2021-4-88-96

Release: 2021-4 (37)

Pages: 88-96

Keywords: sequence interpolation, T-models, Lehmer codes, Catalan, Bell and Stirling numbers of the second kind, q-analogues

Annotation: According to the methodology developed by the author, two one-parameter classes of integer sequences are introduced and investigated in the paper. The first class provides an interpolation between a sequence of powers of two and a sequence of Catalan numbers, and the second class provides an interpolation between a sequence of powers of two and a sequence of Bell numbers. In order to obtain various interpretations of the numbers of the considered classes, T-models and permutations by Lehmer codes are used. These interpretations are based on the recursive construction of sequences of numerical tables of a special kind defining T-models and the properties of permutations by Lehmer codes. The method used leads to simple algorithms for constructing two classes of permutation sets corresponding to the introduced classes of numerical sequences. On the basis of the obtained classes of permutation sets, it is also possible to set probability distributions. The representation of elements of the second class of numerical sequences using Stirling numbers of the second kind allows us to match the class of ordered partitions of sets into a certain number of blocks to the corresponding class of permutation sets. For the numbers of the studied classes of sequences, the relations for their q-analogues are obtained.

Bibliography: Bondarenko L.N. INTERPRETATIONS OF ELEMENTS OF TWO INTERPOLATION CLASSES OF INTEGER SEQUENCES // Education Resources and Technologies. – 2021. – № 4 (37). – С. 88-96. doi: 10.21777/2500-2112-2021-4-88-96