Golnaz Badkobeh

Julien Cassaigne

Michael Rao

Narad Rampersad

Jeffrey Shallit

This is the conjecture presented at WORDS 2007 about infinite binary repetition-free words with minimal letter frequency.

This page is dedicated to the paper Characterization of some binary words with few squares.

Here are the sources of some programs used in the papers

(1) A generator of morphisms for infinite words

(2) A generalization of repetition threshold

(3) Letter frequency in infinite repetition-free words

(4) Upper bound on the number of ternary square-free words

(5) Dejean's conjecture and letter frequency

(6) Avoiding almost squares

(7) Unequal letter frequencies in ternary square-free words

It should compile under linux with a recent enough version of gcc.

It uses GMP.

lib.c, lib.h is a library of functions.

try.c is used to see if an infinite word with some property seems to exist.

gen.c is the generator of morphisms for (1).

gg.c is the generator of morphisms for (2).

check.txt contains the candidate morphisms found by gen.c and gg.c.

check.c checks the properties of the candidate morphisms contained in check.txt.

pow23.c is used to prove that infinite (3,5/3)-free binary words have equal letter frequencies, see (3).

pow.c is used to get lower bounds for rho(q), see (3).

2cuf.c is used to get upper bounds for rho(q+), see (3).

res.txt contains the morphisms found by 2cuf.c.

tara_mor.c checks that the morphisms in (3), th.1 are square-free (uses mreps).

matrix.c is used to obtain an upper bound on the growth rate of ternary square-free words, see (4).

dg-.c and dg+.c are used to find the morphisms in (5).

aas_mul.c is used to find the morphisms avoiding "multiplicative" approximate squares in (6).

aas_add.c is used to find the morphisms avoiding "additive" approximate squares in (6).

unequal.c is used to find the morphisms for ternary square-free words with frequencies (13/45, 1/3, 17/45) and (2/7, 19/56, 3/8) in (7).

weight.c is used to find the negative results in (7).