Selected research results / data / programs
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- 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 N's they are all
binary strings is of some interest as it supports a stronger
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: crochB7.cpp and auxil.h
preliminary versions / genesis of the implementation:
crochB.cpp, crochB1.cpp, crochB2.cpp,
crochB3.cpp, crochB4.cpp,
crochB5.cpp, and crochB6.cpp.
- Erdos' conjecture on multiplicities of compete subgraphs - Jessie Liu's webpage, a Ph.D.
candidate I supervise
- Maximum-number-of-distinct squares conjecture, (d,n-d)
table - Mei
Jiang's webpage, a Ph.D. candidate I supervise
- Maximum-number-of-runs conjecture, (d,n-d) table -
Andrew Baker's webpage, a
Ph.D. candidate I supervise
- 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 (Gd is the set containing the
candidates of length 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, an M.Sc.
candidate I supervise