7 research outputs found
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
Lehmer code transforms and Mahonian statistics on permutations
In 2000 Babson and Steingr{\'\i}msson introduced the notion of vincular
patterns in permutations. They shown that essentially all well-known Mahonian
permutation statistics can be written as combinations of such patterns. Also,
they proved and conjectured that other combinations of vincular patterns are
still Mahonian. These conjectures were proved later: by Foata and Zeilberger in
2001, and by Foata and Randrianarivony in 2006.
In this paper we give an alternative proof of some of these results. Our
approach is based on permutation codes which, like Lehmer's code, map
bijectively permutations onto subexcedant sequences. More precisely, we give
several code transforms (i.e., bijections between subexcedant sequences) which
when applied to Lehmer's code yield new permutation codes which count
occurrences of some vincular patterns
Generalized permutation patterns - a short survey
An occurrence of a classical pattern p in a permutation Ļ is a subsequence of Ļ whose letters are in the same relative order (of size) as those in p. In an occurrence of a generalized pattern, some letters of that subsequence may be required to be adjacent in the permutation. Subsets of permutations characterized by the avoidanceāor the prescribed number of occurrencesā of generalized patterns exhibit connections to an enormous variety of other combinatorial structures, some of them apparently deep. We give a short overview of the state of the art for generalized patterns
Generalized permutation patterns -- a short survey
An occurrence of a classical pattern p in a permutation \pi is a subsequence
of \pi whose letters are in the same relative order (of size) as those in p. In
an occurrence of a generalized pattern, some letters of that subsequence may be
required to be adjacent in the permutation. Subsets of permutations
characterized by the avoidance--or the prescribed number of occurrences--of
generalized patterns exhibit connections to an enormous variety of other
combinatorial structures, some of them apparently deep. We give a short
overview of the state of the art for generalized patterns.Comment: 11 pages. Added a section on asymptotics (Section 8), added more
examples of barred patterns equal to generalized patterns (Section 7) and
made a few other minor additions. To appear in ``Permutation Patterns, St
Andrews 2007'', S.A. Linton, N. Ruskuc, V. Vatter (eds.), LMS Lecture Note
Series, Cambridge University Pres
Two oiseau decompositions of permutations and their application to Eulerian calculus
Abstract: Two transformations are constructed that map the permutation group onto a well-defined subset of a partially commutative monoid generated by the so-called oiseaux. Those transformations are then used to show that some bivariable statistics introduced by Babson and SteingrĆmsson are Euler-Mahonian. 1