9 papers · 1 filter
Even-up words and their variants
Sela Fried
Inspired by OEIS sequence A377912, which consists of the nonnegative integers in which every even digit (except possibly the last) is immediately followed by a strictly larger digi…
Further results on staircase graph words
Sela Fried
Staircase words are words in which consecutive letters do not differ by more than . We generalize this by extending the restriction to letters lying further apart from each othe…
Counting rectangles in nondecreasing and Smirnov words
Sela Fried
The rectangle capacity, a word statistic that was recently introduced by the author and Mansour, counts, for two fixed positive integers and , the number of occurrences of a…
The total number of descents and levels in tensor words and cyclic tensor words
Sela Fried, Toufik Mansour
We obtain an explicit formula for the total number of descents and levels in tensor words and cyclic tensor words of arbitrary dimension. We also establish the exact maximal number…
On the maximal sum of the entries of a matrix power
Sela Fried, Toufik Mansour
Let be the maximal sum of the entries of , where is a square matrix of size , consisting of the numbers , each appearing exactly once. We prove th…
Random Walk Labelings of Perfect Trees and Other Graphs
Sela Fried, Toufik Mansour
A Random walk labeling of a graph is any labeling of that could have been obtained by performing a random walk on . Continuing two recent works, we calculate the number…