Cyclic and Linear Graph Partitions and Normal Ordering
Ken Joffaniel Gonzales
Department of Physical Sciences and Mathematics
University of the Philippines Manila
Manila 1000
Philippines
Abstract:
The Stirling number of a simple graph is the number of partitions of its
vertex set into a specific number of non-empty independent sets. Engbers
et al. showed that the coefficients in the normal ordering of a word
w in
the alphabet {x,D} subject to the relation Dx = xD + 1 are equal to the
Stirling number of certain graphs constructed from w. In this paper, we
introduce graphical versions of the Stirling numbers of the first kind and
the Lah numbers and show how they occur as coefficients in other normal
ordering settings. We also obtain identities involving their q-analogues.
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(Concerned with sequences
A111596
A132393.)
Received June 15 2021; revised version received November 1 2021.
Published in Journal of Integer Sequences,
December 28 2021.
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