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We find a q-analog of the following symmetrical identity involving binomial coefficients n m and Eulerian numbers A n,m , due to Chung, Graham and Knuth [J. k≥0 a + b k A k,a−1 = k≥0 a + b k A k,b−1. We give two proofs, using generating function and bijections, respectively.
The papaya Y-linked region showed clear population structure, resulting in the detection of the ancestral male population that domesticated hermaphrodite papayas were selected from. The same populations were used to study nucleotide diversity and population structure in the X-linked region. Diversity is very low for all genes in the X-linked region in the(More)
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 Stir-ling and Legendre-Stirling numbers. More precisely, letting JS(n + k, n; z) = p k,0 (n) + p k,1 (n)z + · · · + p k,k (n)z k , we show that (1 − t) 3k−i+1 n≥0 p k,i (n)t n is a polynomial in t(More)
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