Noncrossing partitions of an annulus

The noncrossing partition poset associated to a Coxeter group $W$ and Coxeter element $c$ is the interval $[1,c]_T$ in the absolute order on $W$. We construct a new model of noncrossing partititions for $W$ of classical affine type, using planar diagrams (affine types $\tilde A$ and $\tilde C$ in this paper and affine types $\tilde D$ and $\tilde B$ in the sequel). The model in type $\tilde A$ consists of noncrossing partitions of an annulus. In type $\tilde C$, the model consists of symmetric noncrossing partitions of an annulus or noncrossing partitions of a disk with two orbifold points. Following the lead of McCammond and Sulway, we complete $[1,c]_T$ to a lattice by factoring the translations in $[1,c]_T$, but the combinatorics of the planar diagrams leads us to make different choices about how to factor.Comment: 45 pages, 11 figures. Version 2: Minor changes in connection with a revision of arXiv:2212.1379

Acid-insoluble ash is a better indigestible marker than chromic oxide to measure apparent total tract digestibility in pigs

The aim of this study was to determine the apparent total tract digestibility (ATTD) of nutrients in cottonseed meal (CSM) and soybean meal (SBM) in simple carbohydrate and more complex wheat-based diets using 2 indigestible markers and total faecal collection. Twenty-five Large White × Landrace boars (57.8 kg) were randomly allocated to either a pure wheat diet, 40% CSM or SBM in either a sugar-starch- (1:1) or wheat-based diet for 18 d. Acid-insoluble ash (AIA) and chromic oxide (Cr2O3) were included in all diets as indigestible markers. Diets were offered (1,800 g/d per pig) in 3 meals/d from d 1 to 11 and 8 meals/d from d 12 to 17. On d 9, the pigs were moved to individual metabolism cages to allow total faecal collection. On d 18, the pigs were fed hourly for 8 h. After the 8th meal, pigs were anaesthetized and digesta sampled from the terminal ileum and rectum before lethal injection. There were no differences between ATTD of nitrogen (N) determined using AIA as a marker and measured by total faecal collection. On the other hand, the ATTD of N of diets containing CSM in sugar-starch- or wheat-based diets and the pure wheat diet determined using Cr2O3 as a marker was less (−3.11%, −4.46% and −6.59%; P < 0.001) than that measured by total faecal collection. The ATTD of N determined using AIA as a marker was highly correlated with that measured using total faecal collection (P < 0.001; R2 = 0.95). Similarly, the ATTD of N determined using Cr2O3 as a marker was correlated with that measured using total faecal collection, although the correlation was not quite as strong as using AIA (P < 0.001; R2 = 0.87). Also, the slope of the regression line and the intercept were closer to unity and zero for the relationship when the ATTD of N was determined using AIA compared to Cr2O3 as an indigestible marker. The ATTD of organic and dry matter behaved similarly. These data demonstrate that the basal diet and choice of indigestible marker can substantially influence the ATTD and that the use of AIA as an indigestible marker is more suitable than Cr2O3 in digestibility studies in pigs