Sela Fried

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20242026

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9 papers · 1 filter

math.CO2026

Dyck paths on black-and-white lattices

Sela Fried

A Dyck path of semilength $n$ is a lattice path from $(0, 0)$ to $(n, n)$ consisting of $n$ right-steps $(1, 0)$ and $n$ up-steps $(0, 1)$ that never rises above the line $y = x$ . These…

math.CO2026

Proofs of several OEIS conjectures on determinants and permanents

Sela Fried

We prove several conjectures recorded in the On-Line Encyclopedia of Integer Sequences. The conjectures considered here concern determinants and permanents of special matrices, suc…

math.CO2026

Black Cell Capacity in Catalan polyominoes

Jean-Luc Baril, Sela Fried, Nathanaël Hassler +1

A Catalan word is a sequence $w_{1} w_{2} \dots w_{n}$ of nonnegative integers such that $w_{1} = 0$ and $w_{i} \leq w_{i - 1} + 1$ for $2 \leq i \leq n$ . Given a Catalan word, we construct a column…

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…

math.CO2024

Further results on staircase graph words

Sela Fried

Staircase words are words in which consecutive letters do not differ by more than $1$ . We generalize this by extending the restriction to letters lying further apart from each othe…

math.CO2024

Counting $r \times s$ 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 $r$ and $s$ , the number of occurrences of a…

Dyck paths on black-and-white lattices

Proofs of several OEIS conjectures on determinants and permanents

Black Cell Capacity in Catalan polyominoes

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

Further results on staircase graph words

Counting r×s rectangles in nondecreasing and Smirnov words

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

Counting $r \times s$ rectangles in nondecreasing and Smirnov words