3 J an 2 01 2 JACOBI - STIRLING POLYNOMIALS AND P - PARTITIONS IRA
نویسنده
چکیده
Abstract. We investigate the diagonal generating function of the Jacobi-Stirling numbers of the second kind JS(n+ k, n; z) by generalizing the analogous results for the Stirling and Legendre-Stirling numbers. More precisely, letting JS(n + k, n; z) = pk,0(n) + pk,1(n)z + · · ·+ pk,k(n)z , we show that (1− t) ∑ n≥0 pk,i(n)t n is a polynomial in t with nonnegative integral coefficients and provide combinatorial interpretations of the coefficients by using Stanley’s theory of P -partitions.
منابع مشابه
Jacobi-Stirling polynomials and P-partitions
We investigate the diagonal generating function of the Jacobi-Stirling numbers of the second kind JS(n+ k, n; z) by generalizing the analogous results for the Stirling and Legendre-Stirling numbers. More precisely, letting JS(n + k, n; z) = pk,0(n) + pk,1(n)z + · · ·+ pk,k(n)z, we show that (1− t)3k−i+1 ∑ n≥0 pk,i(n)t n is a polynomial in t with nonnegative integral coefficients and provide com...
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