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 ...

This study attempted to identify factors that heiped to explain the subjective well-being of people with spinal cord injury (SCI). A hierarchical multiple regression equation was used to determine the proportion of observed variance in the subjective well-being explained by the independent variables (perceived freedom in leisure, free time boredom, frequency of recreation participation, watchin...

Indigenous people are the most underrepresented racial/ethnic group in Science, Technology, Engineering, Mathematics, and Medicine (STEMM) United States. Most prior research suggests this trend is result broadly of settler colonialism, more specifically cultural differences between students school/university environments; poor academic preparation K-12 schools; vague constructs educational or v...