4 papers
Counting k-ary words by number of adjacency differences of a prescribed size
Sela Fried, Toufik Mansour, Mark Shattuck
Recently, the general problem of enumerating permutations such that for all , where and are fixed, was considered by…
Counting rectangles in (Catalan) words
Sela Fried, Toufik Mansour
Generalizing previous results, we introduce and study a new statistic on words, that we call rectangle capacity. For two fixed positive integers and , this statistic counts…
Staircase graph words
Sela Fried, Toufik Mansour
Generalizing the notion of staircase words, introduced by Knopfmacher et.\ al, we define staircase graph words. These are functions from the vertex set of a graph into the…
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…