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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2024-11-01
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| author | Adnan Hashim Abdulwahid |
| author_facet | Adnan Hashim Abdulwahid |
| author_sort | Adnan Hashim Abdulwahid |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-7e4c83a6c0dc42488e8e9821eaa61982 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-7e4c83a6c0dc42488e8e9821eaa619822024-11-26T18:12:04ZengMDPI AGMathematics2227-73902024-11-011222362110.3390/math12223621Partition Differential Equations and Some Combinatorial Algebraic StructuresAdnan Hashim Abdulwahid0College of Business, Engineering, and Technology, Texas A&M University–Texarkana, 7101 University Ave, Texarkana, TX 75503, USALet <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.https://www.mdpi.com/2227-7390/12/22/3621partitionsderivativeintegralsymmetric functionscoalgebraStirling |
| spellingShingle | Adnan Hashim Abdulwahid Partition Differential Equations and Some Combinatorial Algebraic Structures Mathematics partitions derivative integral symmetric functions coalgebra Stirling |
| title | Partition Differential Equations and Some Combinatorial Algebraic Structures |
| title_full | Partition Differential Equations and Some Combinatorial Algebraic Structures |
| title_fullStr | Partition Differential Equations and Some Combinatorial Algebraic Structures |
| title_full_unstemmed | Partition Differential Equations and Some Combinatorial Algebraic Structures |
| title_short | Partition Differential Equations and Some Combinatorial Algebraic Structures |
| title_sort | partition differential equations and some combinatorial algebraic structures |
| topic | partitions derivative integral symmetric functions coalgebra Stirling |
| url | https://www.mdpi.com/2227-7390/12/22/3621 |
| work_keys_str_mv | AT adnanhashimabdulwahid partitiondifferentialequationsandsomecombinatorialalgebraicstructures |