Partition Differential Equations and Some Combinatorial Algebraic Structures - Adnan Hashim Abdulwahid (Mathematics)
Let <semantics>Λ</semantics> 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 <semantics>Λ</semantics>, and it characterizes the primitive elements in <semantics>Λ</semantics> using the Jacobian determinants of partition primitive functions.