1,410 research outputs found
Snow Leopard Permutations and Their Even and Odd Threads
Caffrey, Egge, Michel, Rubin and Ver Steegh recently introduced snow leopard
permutations, which are the anti-Baxter permutations that are compatible with
the doubly alternating Baxter permutations. Among other things, they showed
that these permutations preserve parity, and that the number of snow leopard
permutations of length is the Catalan number . In this paper we
investigate the permutations that the snow leopard permutations induce on their
even and odd entries; we call these the even threads and the odd threads,
respectively. We give recursive bijections between these permutations and
certain families of Catalan paths. We characterize the odd (resp. even) threads
which form the other half of a snow leopard permutation whose even (resp. odd)
thread is layered in terms of pattern avoidance, and we give a constructive
bijection between the set of permutations of length which are both even
threads and odd threads and the set of peakless Motzkin paths of length .Comment: 25 pages, 6 figures. Version 3 is modified to use standard Discrete
Mathematics and Theoretical Computer Science but is otherwise unchange
The Probability of a Basketball Rebounding in Specific Areas After a Missed Shot is Taken from a Certain Area
Rebounding in basketball has always been of concern and importance to coaches at all levels of competition. The collection of data concerning on-the-court performance of basketball players has increased greatly during the past twelve years; however, only limited rebounding statistics have appeared in recent studies. Allsen concluded that shots attempted from the right side have a tendency to rebound to the middle and right side. On the other hand, when shots were attempted from the left side a greater percentage of missed shots rebounded to the right side or middle area of the court. In Allsen\u27s study there was equal importance placed on recording the area the unsuccessful shots were attempted from as well as what area the ball became available for rebounding. Huberty, however, stated that there have been no studies of significance completed concerning the probability of a ball rebounding in a specific area of the basketball court after an unsuccessful shot. In basketball circles it is stated “the team that controls the boards controls the game.” Accordingly, there is a need to know, if possible, in what area of the basketball floor a ball will fall after an unsuccessful shot from certain areas of the court is taken. Coaches need to have proper on-the-court organization to put players in position to get rebounds. As a player and coach of basketball, the investigator became interested in attempting to formulate offense and defense rebounding team strategy which could be useful to the basketball coaching profession. Information obtained from the current study could serve as a basis for such rebounding strategy. The purpose of the study was to determine the probability of where, in a specific area of the basketball court, a ball will be rebounded after an unsuccessful shot taken from a certain area of the court
- …