Generalized Sequential-Selection Formula for Structured Digit Permutations
Year: 2026
Type: article
Abstract: This paper introduces a unified sequential-selection formula for calculating the total number of N-digit positive integers with specific structural digit frequencies (e.g., AABB, AAAB, AABBCC). By integrating sequential digit choices (9 \times 9 \times 8 \dots), multiset permutations, and a symmetry-reduction factor \frac{1}{k!}, the proposed method simplifies counting across equal-frequency digit roles. This approach handles both multiset role symmetry and leading-zero exclusions in a single calculation, eliminating the need for extensive case analysis. Includes detailed derivations, worked examples, and a summary reference table.
Author: Achit Bhatia
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203874301
FWCI:
Cites:
Cited by:
Related to: