# TRANSFORMATIONS OF COMBINATORIAL SEQUENCES AND T-MODELS

**Author(s):**
Bondarenko L.N.

**Rubric:**
Mathematical cybernetics

**DOI: **
10.21777/2500-2112-2020-3-89-97

**Release:**
2020-3 (32)

**Pages:**
89-97

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

**Annotation:**
This article continues the discussion of issues related to the modeling, classification and standardization of combinatorial sequences. T-models and T-diagrams are used for this. The T-model is a sequence of tables of a special kind made up of positive integers. It is obtained using a simple algorithm, and easily corresponded to a combinatorial sequence. In some cases, the T-model can be used to build a T-diagram, which is a Hasse diagram of a partially ordered set simply associated with a T-model. For a T-diagram, two two-index sequences are introduced, closely related to the corresponding combinatorial sequence. This makes it possible to study as single-index but double-index sequences. In this paper, using some transformations of combinatorial sequences, classes of T-models are introduced. In some cases, these classes simplify methods of modeling and classification for combinatorial sequences. The problem of using such classes of T-models to obtain new combinatorial results is considered.

**Bibliography:**
Bondarenko L.N. TRANSFORMATIONS OF COMBINATORIAL SEQUENCES AND T-MODELS // Education Resources and Technologies. – 2020. – № 3 (32). – С. 89-97. doi: 10.21777/2500-2112-2020-3-89-97