A Combinatorial Approach to the Stirling Numbers of the First Kind with Higher Level
2021 ◽
Vol 58
(3)
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pp. 293-307
Keyword(s):
In this paper, we investigate a generalization of the classical Stirling numbers of the first kind by considering permutations over tuples with an extra condition on the minimal elements of the cycles. The main focus of this work is the analysis of combinatorial properties of these new objects. We give general combinatorial identities and some recurrence relations. We also show some connections with other sequences such as poly-Cauchy numbers with higher level and central factorial numbers. To obtain our results, we use pure combinatorial arguments and classical manipulations of formal power series.
2018 ◽
Vol 14
(05)
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pp. 1211-1222
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Keyword(s):
2018 ◽
Vol 12
(1)
◽
pp. 1-35
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Keyword(s):
2003 ◽
Vol 184
(2)
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pp. 369-383
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Keyword(s):
2004 ◽
Vol 339
(8)
◽
pp. 533-538
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2002 ◽
Vol 51
(3)
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pp. 403-410
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