Список литературы

2518-1092

Research result. Information technologies

2518-1092

10.18413/2518-1092-2026-11-3-0-9

4362

COMPUTER SIMULATION

<strong>DESCRIPTION OF A COMBINATORIAL ALGORITHM FOR ENUMERATING ORDERED MULTIPLICATIVE FACTORIZATIONS</strong>

Rumbesht

Vadim Валерьевич

Rumbesht

Vadim Валерьевич

rumbesht@bsuedu.ru

Burdanova

Ekaterina Vasilyevna

Burdanova

Ekaterina Vasilyevna

burdanova@bsuedu.ru

2026

11300

The article is devoted to solving a typical combinatorial problem – a systematic enumeration of all objects of a certain type. The decomposition of an integer  into an ordered product of integer multipliers (the so-called -profile of number ) is accepted as an object for enumeration. The purpose of the article is to create a combinatorial algorithm for the systematic enumeration of all -profiles of number . To achieve this goal, a formal formulation of the problem was carried out, its analysis was carried out, in which the concept of a characteristic matrix of -profile  was introduced and a one-to-one correspondence between profiles and characteristic matrices was established, which made it possible to move from enumerating profiles to enumerating characteristic matrices, followed by their transformation into profiles. An -equivalence relation is introduced on the set of characteristic matrices, which makes it possible to divide it into classes and list the elements of the selected -equivalence class independently of the rest of the characteristic matrices. It is shown that the generation of an -equivalent characteristic matrix is the process of determining its elements by distributing units of multiplicities of prime factors in the canonical expansion of a number , and this process is considered in detail. At the synthesis stage, the results of the task analysis are translated into the desired algorithm. An example of enumeration -profiles of number  using this algorithm is given.

ordered multiplicative decompositionn-profile of number rcombinatorial algorithmsystematic enumerationcharacteristic matrix of n-profile of rdistribution process

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