Partition Differential Equations and Some Combinatorial Algebraic Structures

Adnan Hashim Abdulwahid ()
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Adnan Hashim Abdulwahid: College of Business, Engineering, and Technology, Texas A&M University–Texarkana, 7101 University Ave, Texarkana, TX 75503, USA

Mathematics, 2024, vol. 12, issue 22, 1-18

Abstract: Let Λ be the algebra of symmetric functions. We introduce Stirling partitions, factorial partition polynomials, partition differential equations and their corresponding partitions, and partition primitive functions. Most importantly, this investigation provides a new combinatorial coalgebra structure on Λ , and it characterizes the primitive elements in Λ using the Jacobian determinants of partition primitive functions.

Keywords: partitions; derivative; integral; symmetric functions; coalgebra; Stirling (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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