Selected research results / data / programs Home

- A space efficient implementation of Crochemore's repetitions algorithm in C
- 2-factorizations of K9
- 2-factorizations of K11 (corrected)
- 192 known KTS(21)
- 2-factorizations of K13
- Run-maximal strings for lengths 2 to 35, a
complete enumeration (only lexicographically smallest strings are listed,

i.e. the inverted strings are not listed), all the runs are listed as well. These result were obtained independently of

the alphabet; the fact that for bigger's they are all binary strings is of some interest as it supports a stronger**N**

hypothesis than that.**for every N, there is a binary string that admits the maximum number of runs** - A program to compute maximal repetitions, runs, and distinct squares in a string
based on Crochemore's

portioning algorithm, implemented in C++ by Franek, Jiang, and Weng

complete final version with memory saving techniques: crochB7.cpp and auxil.h

original version without memory saving tachniques: crochB.cpp - Erdos' conjecture on multiplicities of compete subgraphs - Jessie Liu's webpage
- Maximum-number-of-distinct squares conjecture, (
*d*,*n*-*d*) table - Mei Jiang's webpage - Maximum-number-of-runs conjecture, (
*d*,*n*-*d*) table - Andrew Baker's webpage - R-cover and structure of run-maximal strings, a C++ program to generate candidates
for run-maximal strings using the R-cover property: rcover.cpp,
crochB7.hpp, auxil.h

Generating candidates for run-maximal binary strings of length 35, the following sets were generated in 19 minutes (is the set containing the candidates of length**Gd****d**

G4, G5, G6, G7, G8, G9, G10, G11, G12, G13, G14, G15, G16, G17, G18, G19, G20, G21, G22, G23, G24, G25, G26, G27, G28, G29, G30, G31, G32, G33, G34 and G35 - C/C++ linear implementation of runs algorithm by C. Weng - Chia-Chun (Jasper) Weng's webpage
- C++ source code ub.cpp for computing a sorted Lyndon
array from a partially sorted Lyndon array, see F. Franek, A. Paracha, and W.F. Smyth:
*The Linear Equivalence of the Suffix Array and the Partially Sorted Lyndon Array*, Proceedings of Prague Stringology Conference PSC 2017, Prague, Czech Republic, August, 2017, pp 77-84. - C++ source code for
algorithm to compute Lyndon array of a string (previously denoted as BLS): bsla.cpp, Lstring.hpp, lynarr.hpp, makefile*BSLA* - C++ source code for
algorithm to compute Lyndon array of a string (previously denoted as LPF): trla.cpp, Tau.hpp, Lstring.hpp, lynarr.hpp, debug.hpp, makefile**TRLA** - C++ source code for
algorithm to compute Lyndon array of a string: lynarr.hpp**IDLA** - C++source code for Rauzy graph and computation of cycles in all its components, and computing of Φ(uu) for any square, authors F. Franek and H. Koponen: rauzy.cpp