| In this thesis,we investigate two problems relative to Rota-Baxter algebras.For the first problem,we study the stuffle product by order preserving maps,and give a direct proof that it satisfies the commutativity and associativity.By using generating functions and Delannoy paths,we give the number of the terms in the sum defining aⅢst,λbⅢst,λ c.It is well-known that Stirling numbers are closely re-lated to Rota-Baxter algebras.For the second problem,we carry out an analogous study for modified Rota-Baxter algebras.We give an interpretation of modified Stirling numbers of the second kind in terms of modified Rota-Baxter algebras,and give a relationship between modified Stirling numbers and Stirling numbers.A recursive formula for modified Stirling numbers is given. |
