Walks, Partitions, and Normal Ordering

Askar Dzhumadil'daev, Damir Yeliussizov


We describe the relation between graph decompositions into walks and the normal ordering of differential operators in the $n$-th Weyl algebra. Under several specifications, we study new types of restricted set partitions, and a generalization of Stirling numbers, which we call the $\lambda$-Stirling numbers.


Walks, Differential operators, Weyl algebra, Set partitions, Stirling numbers

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