Sela Fried

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math.CO2025

Black-White Cell Capacity in $k$ -ary Words and Permutations

Sela Fried

We introduce a new bargraph statistic that we call black-white cell capacity. It is obtained by coloring the cells of the bargraph in a chessboard style and recording the numbers o…

math.CO2025

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…

math.CO2025

A formula for the number of up-down words

Sela Fried

A word $w_{1} w_{2} \dots w_{n}$ is said to be up-down if $w_{1} < w_{2} > w_{3} \dots$ . Carlitz and Scoville found the generating function for the number of up-down words over an alphabet of s…

math.CO2025

Further results on staircase (cyclic) words

Sela Fried

We find the two-variables generating function for the statistic which counts the number of variations in a word bounded by $1$ . Thus, we refine and extend previous results concerni…

Black-White Cell Capacity in k-ary Words and Permutations

Even-up words and their variants

A formula for the number of up-down words

Further results on staircase (cyclic) words

Black-White Cell Capacity in $k$ -ary Words and Permutations