### Some partition problems related to the Stirling numbers of the second kind

L. Carlitz (1965)

Acta Arithmetica

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L. Carlitz (1965)

Acta Arithmetica

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D. V. Lee (1992)

Acta Arithmetica

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Introduction. The problem of determining the formula for ${P}_{S}\left(n\right)$, the number of partitions of an integer into elements of a finite set S, that is, the number of solutions in non-negative integers, ${h}_{s\u2081},...,{h}_{{s}_{k}}$, of the equation hs₁ s₁ + ... + hsk sk = n, was solved in the nineteenth century (see Sylvester [4] and Glaisher [3] for detailed accounts). The solution is the coefficient of$x\u207fin$[(1-xs₁)... (1-xsk)]-1, expressions for which they derived. Wright [5] indicated a simpler method by which to find part...

L. Carlitz (1976)

Collectanea Mathematica

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L. Carlitz, S. Klamkin (1974)

Collectanea Mathematica

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L. Carlitz (1973)

Rendiconti del Seminario Matematico della Università di Padova

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Carlitz, L. (1953)

Portugaliae mathematica

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Jaroslav Hančl (1996)

Journal de théorie des nombres de Bordeaux

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We generalize a previous result due to Badea relating to the irrationality of some quick convergent infinite series.

Josef Kaucký (1968)

Matematický časopis

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Carlitz, L. (1956)

Portugaliae mathematica

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