T-MODELS APPLICATION FOR INTEGER SEQUENCES INTERPOLATION

Author(s): Bondarenko L.N.

Rubric: Methodological research

DOI: 10.21777/2500-2112-2021-3-97-105

Release: 2021-3 (36)

Pages: 97-105

Keywords: sequence interpolation, T-models, Lehmer codes, generalized Catalan numbers, generalized Bell numbers, qanalogue

Annotation: The article proposes a new technique for interpolating integer sequences. It is demonstrated on classes interpolating sequences between Catalan numbers and factorials and between Bell numbers and factorials as well. This technique is based on T-models and Lehmer permutations codes. T-models are specified recursively by sequences of special type numerical tables. It allows us to obtain algorithms for solving a number of emerging problems. Integer sequences correspond to T-models whereas sets of numbers (codes) of their elements are also constructed for the latter. Using this technique the article introduces the classes of generalized Catalan and Bell numbers, as well as their q-analogues. Their extension leads to the sequence interpolation problem solution. We also find the permutation classes corresponding to sequences and given by sets of Lehmer codes. This approach greatly simplifies the construction of permutation classes that were previously obtained in computer science articles by means of removing the permutations with given patterns.

Bibliography: Bondarenko L.N. T-MODELS APPLICATION FOR INTEGER SEQUENCES INTERPOLATION // Education Resources and Technologies. – 2021. – № 3 (36). – С. 97-105. doi: 10.21777/2500-2112-2021-3-97-105