Work

Direct Closed-Form Cardinalities for Bounded Multisubset Classes

Year: 2026

Type: preprint

Abstract: This paper provides a direct, non-recursive mathematical framework to determine the exact cardinality of multisubsets derived from a regular parent multiset M=(r^n). Extending the combinatorial foundations of Singh and Singh (2003), we partition the submultiset space into eight distinct, disjoint classes using element repetition (R/NR) and identity/order (B/NB) configurations. We derive explicit, closed-form formulas for each and all of these eight classes. Using only the parent parameters n and r, these formulas instantly calculate class cardinalities, bypassing computationally heavy generating function expansions and manual partition groupings.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.21016762

Author: Aminu, SAMSON Imoleayo

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7166564064

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