Partition Differential Equations and Some Combinatorial Algebraic Structures

Partition Differential Equations and Some Combinatorial Algebraic Structures

Let <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="normal">Λ</mi></semantics></math></inline-formula> be the algebra of symmetric functions. We introduce Stirl...

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Bibliographic Details
Main Author:	Adnan Hashim Abdulwahid
Format:	Article
Language:	English
Published:	MDPI AG 2024-11-01
Series:	Mathematics
Subjects:	partitions derivative integral symmetric functions coalgebra Stirling
Online Access:	https://www.mdpi.com/2227-7390/12/22/3621
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Summary:	Let <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="normal">Λ</mi></semantics></math></inline-formula> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="normal">Λ</mi></semantics></math></inline-formula>, and it characterizes the primitive elements in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="normal">Λ</mi></semantics></math></inline-formula> using the Jacobian determinants of partition primitive functions.
ISSN:	2227-7390