广义Bell和Stirling数的组合方法与玻色子正规序问题
Combinatorial approach to generalized Bell and Stirling numbers and boson normal ordering problem
摘要：
我们考虑在规范玻色子创造和湮灭运营商的正常秩序的表达问题中出现的数字。我们对待的玻色子弦的一般形式，这是与斯特林和贝尔数的推广。这些量的递归关系和封闭形式的表达式（Dobiski型公式）得到的代数和组合的方法。通过广泛使用组合分析的方法，我们证明了上述问题的等价性特殊的图族的计数。这个链接提供了在这个正常排序问题中出现的数字的组合解释。
英文摘要：
We consider the numbers arising in the problem of normal ordering of expressions in canonical boson creation and annihilation operators. We treat a general form of a boson string which is shown to be associated with generalizations of Stirling and Bell numbers. The recurrence relations and closed-form expressions (Dobiski-type formulas) are obtained for these quantities by both algebraic and combinatorial methods. By extensive use of methods of combinatorial analysis we prove the equivalence of the aforementioned problem to the enumeration of special families of graphs. This link provides a combinatorial interpretation of the numbers arising in this normal ordering problem.
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