Patterns in Inversion Sequences I

Permutations that avoid given patterns have been studied in great depth for their connections to other fields of mathematics, computer science, and biology. From a combinatorial perspective, permutation patterns have served as a unifying interpretation that relates a vast array of combinatorial structures. In this paper, we introduce the notion of patterns in inversion sequences. A sequence $(e_1,e_2,\ldots,e_n)$ is an inversion sequence if $0 \leq e_i<i$ for all $i \in [n]$. Inversion sequences of length $n$ are in bijection with permutations of length $n$; an inversion sequence can be obtained from any permutation $\pi=\pi_1\pi_2\ldots \pi_n$ by setting $e_i = |\{j \ | \ j \pi_i \}|$. This correspondence makes it a natural extension to study patterns in inversion sequences much in the same way that patterns have been studied in permutations. This paper, the first of two on patterns in inversion sequences, focuses on the enumeration of inversion sequences that avoid words of length three. Our results connect patterns in inversion sequences to a number of well-known numerical sequences including Fibonacci numbers, Bell numbers, Schr\"oder numbers, and Euler up/down numbers

Ischemic preconditioning improves maximal performance in humans

Repeated episodes of ischemia followed by reperfusion, commonly referred to as ischemic preconditioning (IPC), represent an endogenous protective mechanism that delays cell injury. IPC also increases blood flow and improves endothelial function. We hypothesize that IPC will improve physical exercise performance and maximal oxygen consumption. The purpose of the study was to examine the effect of ischemic preconditioning in leg skeletal muscles on cycling exercise performance in healthy individuals. Fifteen healthy, well-trained subjects performed two incremental maximal exercise tests on a bicycle ergometer. Power output, oxygen consumption, ventilation, respiratory quotient, and heart rate were measured continuously. Blood pressure and blood lactate were measured before and after the test. One exercise test was performed after the application of ischemic preconditioning, using a protocol of three series of 5-min ischemia at both legs with resting periods of 5 min in between. The other maximal cycling test served as a control. Tests were conducted in counterbalanced order, at least 1 week apart, at the same time of the day. The repeated ischemic periods significantly increased maximal oxygen consumption from 56.8 to 58.4 ml/min per kg (P = 0.003). Maximal power output increased significantly from 366 to 372 W (P = 0.05). Ischemic preconditioning had no effect on ventilation, respiratory quotient, maximal heart rate, blood pressure or on blood lactate. Repeated short-term leg ischemia prior to an incremental bicycle exercise test improves maximal oxygen consumption by 3% and power output by 1.6%. This protocol, which is suggested to mimic the effects of ischemic preconditioning, may have important implications for exercise performance