Sela Fried

activity

20242026

collaborators

11 papers

math.GM2026

Further proofs of conjectures from the OEIS

Sela Fried

This is the fourth work in a series devoted to proving conjectures recorded in the On-Line Encyclopedia of Integer Sequences (OEIS). The problems considered here concern elementary…

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.NT2024

Proofs of some Conjectures from the OEIS

Sela Fried

In this work we resolve several conjectures stated in the On-Line Encyclopedia of Integer sequences.

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…

Further proofs of conjectures from the OEIS

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

Proofs of some Conjectures from the OEIS

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