The Subset Size Sum Sequence: Structural Properties and Mathematical Applications
DOI:
https://doi.org/10.5281/zenodo.21337409Keywords:
Subset Size Sum Sequence, Combinatorics, Discrete mathematics, Integer sequences, Generating functions, Graph theoryAbstract
The Subset Size Sum Sequence is defined as the sum of the cardinalities of all subsets of an -element set. This study establishes its closed form and investigates its fundamental properties, including recurrence relations, generating functions, and relationships with known integer sequences. Furthermore, applications in combinatorics, graph theory, and discrete mathematics are presented. The findings demonstrate that the sequence provides a unified counting interpretation across various mathematical structures.
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