# MODELING OF COMBINATOR SEQUENCES

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

**Rubric:**
Mathematical cybernetics

**DOI: **
10.21777/2500-2112-2019-2-64-73

**Release:**
2019-2 (27)

**Pages:**
64-73

**Keywords:**
T-model, T(q)-model, poset, T-diagram, distributive lattice, generalized factorials, Catalan numbers, Bell numbers, Lehmer codes, RG-words

**Annotation:**
The method of modeling combinatorial sequences using special sequences of tables consisting of positive integers is considered. These sequences are called T-models and are constructed recursively using special mappings. For T-models, q-analogues are introduced, which allow modeling the q-analogs of combinatorial sequences corresponding to them. Partially ordered sets and the corresponding T-diagrams are also defined. With the help of these partially ordered sets and T-diagrams, numerous additional properties of the simulated combinatorial sequences are considered. Examples of T-models of sequences of generalized factorials, Catalan numbers and Bell numbers are given. Their q-analogues and T-diagrams are constructed. This makes it possible to investigate also the properties of balloting numbers, Stirling numbers of the second kind and their q-analogues. The structure of T-models of combinatorial sequences makes it possible to use the well-known analytical calculation packages Mathematica and Maple in their modeling. Therefore, T-models can be used in teaching students to separate sections of discrete mathematics and computer science, as well as to obtain with their help combinatorial results.

**Bibliography:**
Bondarenko LE.NI. MODELING OF COMBINATOR SEQUENCES // Education Resources and Technologies. – 2019. – № 2 (27). – С. 64-73. doi: 10.21777/2500-2112-2019-2-64-73