18 research outputs found
A q-analog of the Seidel generation of Genocchi numbers
A new -analog of Genocchi numbers is introduced through a q-analog of
Seidel's triangle associated to Genocchi numbers. It is then shown that these
-Genocchi numbers have interesting combinatorial interpretations in the
classical models for Genocchi numbers such as alternating pistols, alternating
permutations, non intersecting lattice paths and skew Young tableaux.Comment: 17 page
Genocchi Numbers and f-Vectors of Simplicial Balls
The Genocchi numbers are the coefficients of the generating function
2t/(e^t+1). In this note we will give an equation for simplicial balls which
involves this numbers. It relates the number of faces in the interior of the
ball with the number of faces in the boundary of the ball. This is a variation
of similar equations given in [McMullen 2004] and [Herrmann and Joswig 2006].Comment: revised version, to appear in European Journal of Combinatorics;
minor change
Combinatorial proofs of some properties of tangent and Genocchi numbers
The tangent number is equal to the number of increasing labelled
complete binary trees with vertices. This combinatorial interpretation
immediately proves that is divisible by . However, a stronger
divisibility property is known in the studies of Bernoulli and Genocchi
numbers, namely, the divisibility of by . The
traditional proofs of this fact need significant calculations. In the present
paper, we provide a combinatorial proof of the latter divisibility by using the
hook length formula for trees. Furthermore, our method is extended to -ary
trees, leading to a new generalization of the Genocchi numbers
Combinatorial study of the Dellac configurations and the q-extended normalized median Genocchi numbers
In two recent papers (\textit{Mathematical Research Letters,18(6):1163--1178,2011} and \textit{European J. Combin.,33(8):1913--1918,2012}), Feigin proved that the Poincaré polynomials of the degenerate flag varieties have a combinatorial interpretation through the Dellac configurations, and related them to the -extended normalized median Genocchi numbers introduced by Han and Zeng, mainly by geometric considerations. In this paper, we give combinatorial proofs of these results by constructing statistic-preserving bijections between the Dellac configurations and two other combinatorial models of
European Journal of Combinatorics Index, Volume 27
BACKGROUND: Diabetes is an inflammatory condition associated with iron abnormalities and increased oxidative damage. We aimed to investigate how diabetes affects the interrelationships between these pathogenic mechanisms. METHODS: Glycaemic control, serum iron, proteins involved in iron homeostasis, global antioxidant capacity and levels of antioxidants and peroxidation products were measured in 39 type 1 and 67 type 2 diabetic patients and 100 control subjects. RESULTS: Although serum iron was lower in diabetes, serum ferritin was elevated in type 2 diabetes (p = 0.02). This increase was not related to inflammation (C-reactive protein) but inversely correlated with soluble transferrin receptors (r = - 0.38, p = 0.002). Haptoglobin was higher in both type 1 and type 2 diabetes (p < 0.001) and haemopexin was higher in type 2 diabetes (p < 0.001). The relation between C-reactive protein and haemopexin was lost in type 2 diabetes (r = 0.15, p = 0.27 vs r = 0.63, p < 0.001 in type 1 diabetes and r = 0.36, p = 0.001 in controls). Haemopexin levels were independently determined by triacylglycerol (R(2) = 0.43) and the diabetic state (R(2) = 0.13). Regarding oxidative stress status, lower antioxidant concentrations were found for retinol and uric acid in type 1 diabetes, alpha-tocopherol and ascorbate in type 2 diabetes and protein thiols in both types. These decreases were partially explained by metabolic-, inflammatory- and iron alterations. An additional independent effect of the diabetic state on the oxidative stress status could be identified (R(2) = 0.5-0.14). CONCLUSIONS: Circulating proteins, body iron stores, inflammation, oxidative stress and their interrelationships are abnormal in patients with diabetes and differ between type 1 and type 2 diabetes</p