Record number :
Title of article :
Reciprocity for multirestricted Stirling numbers
Author/Authors :
Choi، نويسنده , , Ji Young and Long، نويسنده , , Ling Kok Ng، نويسنده , , Siu-Hung and Smith، نويسنده , , Jonathan، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2006
Pages :
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Abstract :
Multirestricted Stirling numbers of the second kind count the number of partitions of a given set into a given number of parts, each part being restricted to at most a fixed number of elements. Multirestricted numbers of the first kind are then defined as elements of the matrix inverse to the matrix of corresponding multirestricted numbers of the second kind. The anomalous sign behavior of these latter numbers makes them impervious to combinatorial analysis. In answer to a conjecture that has remained open for several years, we derive a reciprocity law for multirestricted Stirling numbers using algebraic techniques based on polynomial recursions. As corollaries, we obtain new recurrence relations for multirestricted numbers, and a new algebraic derivation of the reciprocity law for Stirling numbers.
Keywords :
Stirling number , Bessel number , Multirestricted number , Differentiably finite , Polynomially recursive , Reciprocity relation , Topological basis
Journal title :
Journal of Combinatorial Theory Series A
Journal title :
Journal of Combinatorial Theory Series A
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