# SYSTEMATIZATION OF COMBINATOR SEQUENCES USING T-MODELS AND T-DIAGRAMS

**Author(s):**
Bondarenko Leonid Nikolaevich

**DOI: **
10.21777/2500-2112-2020-2-58-68

**Release:**
2020-2 (31)

**Pages:**
58-68

**Keywords:**
Systematization, classification, combinatorial sequence, T-model, poset, T-diagram, generating function

**Annotation:**
To systematize combinatorial sequences, as well as the associated to them two-index sequences, T-models and T-diagrams are used. T-models are sequences of numerical tables of a peculiar kind, and T-diagrams are Hasse diagrams based on these tables. Defining the T-model with a set of alphabet, special mapping, and initial table makes it easy to obtain classes of T-models and T-diagrams by introducing parameters. Comparison of these classes by the type of special mapping makes it possible to construct their systematization. As an example, the article gives a systematization of classes of degrees, generalized factorials, generalized Fibonacci numbers, Catalan numbers and Bell numbers, as well as some other classes of generalized numbers that are simply systematized by this method.

**Bibliography:**
Bondarenko LE.NI. SYSTEMATIZATION OF COMBINATOR SEQUENCES USING T-MODELS AND T-DIAGRAMS // Education Resources and Technologies. – 2020. – № 2 (31). – С. 58-68. doi: 10.21777/2500-2112-2020-2-58-68