11 papers
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…
Dyck paths on black-and-white lattices
Sela Fried
A Dyck path of semilength is a lattice path from to consisting of right-steps and up-steps that never rises above the line . These…
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…
Black Cell Capacity in Catalan polyominoes
Jean-Luc Baril, Sela Fried, Nathanaël Hassler +1
A Catalan word is a sequence of nonnegative integers such that and for . Given a Catalan word, we construct a column…
Black-White Cell Capacity in -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…
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…
A formula for the number of up-down words
Sela Fried
A word is said to be up-down if . Carlitz and Scoville found the generating function for the number of up-down words over an alphabet of s…
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 . Thus, we refine and extend previous results concerni…
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…
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.
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…