Generalized Sequential-Selection Formula for Structured Digit Permutations

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.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-08-20
DOI
https://doi.org/10.5281/zenodo.22031374
Primary Topic
Benford’s Law and Fraud Detection
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

Generalized Sequential-Selection Formula for Structured Digit Permutations

Achit Bhatia
Zenodo (CERN European Organization for Nuclear Research)
Benford’s Law and Fraud Detection
article

Generalized Sequential-Selection Formula for Structured Digit Permutations

Achit Bhatia
article en

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.

Zenodo (CERN European Organization for Nuclear Research)
Reduced inequalities
Openalex Percentile: Top 7%
Benford’s Law and Fraud Detection
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.