We survey three recent breakthroughs in algebraic combinatorics. The first is the proof by Knutson and Tao, and later Derksen and Weyman, of the saturation conjecture for Littlewood-Richardson coefficients. The second is the proof of the n! and (n + 1)n−1 conjectures by Haiman. The final breakthrough is the determination by Baik, Deift, and Johansson of the limiting behavior of the length of th...

Let u(d, n) denote the number of permuations in the symmetric group Sn with no increasing subsequence of length greater than d. u(d, n) may alternatively be interpreted as the number of closed Z-lattice walks which begin and end at the origin and take n positive steps followed by n negative steps while remaining confined to the Weyl chamber W = {(t1, t2, . . . , td) ∈ R : t1 ≥ t2 ≥ · · · ≥ td}....

Karlin and Altschul in their statistical analysis for multiple highscoring segments in molecular sequences introduced a distribution function which gives the probability there are at least r distinct and consistently ordered segment pairs all with score at least x. For long sequences this distribution can be expressed in terms of the distribution of the length of the longest increasing subseque...

The Mallows measure on the symmetric group Sn is the probability measure such that each permutation has probability proportional to q raised to the power of the number of inversions, where q is a positive parameter and the number of inversions of π is equal to the number of pairs i < j such that πi > πj . We prove a weak law of large numbers for the length of the longest increasing subsequence ...

OBJECTIVE The objective of the study was to determine the effects of increasing levels of metabolizable protein (MP) on lactation performance and nitrogen (N) efficiencies in lactating dairy cows. METHODS Nine multiparous cows in mid lactation [113±25 days in milk] received three treatments in a 3×3 Latin square design with a period length of 21 days. The treatments were three diets, designed...

0167-9317/$ see front matter 2011 Elsevier B.V. A doi:10.1016/j.mee.2011.08.004 ⇑ Corresponding author. Tel.: +1 517 432 2130. E-mail address: [email protected] (N. Sepúlved This paper reports a multiple-state micro-mechanical memory. The tip displacements of a 350 lm long VO2-coated micro-mechanical silicon cantilever were programmed to absolute displacements ranging from 19 to 7 m. Ten non-...

theaim of the current study was to assess effects of different levels of origanum vulgare (0, 250, 500, 750 and 1000 mg/l) on kinetics of gas production, some ruminal digestion and fermentation parameters, methane production and also to determine its potential in controlling rumen acidosis using in vitro method in four separate phases. in the first phase, the asymptote of gas production (a) and...

Effects of monensin (MON) and S on in vitro fermentation and H(2)S production were evaluated in 2 experiments. In Exp. 1, 2 ruminally cannulated steers were adapted (>14 d) to a 75% concentrate diet [steam-flaked corn (SFC)-based], and ruminal fluid was collected approximately 4 h after feeding. Substrate composed (DM basis) of 85.2% SFC, 9% alfalfa hay, 5% cottonseed meal, and 0.8% urea was ad...