References
- Alon, N., D. Elboim, J. Pach, and G. Tardos. 2021. Random necklaces require fewer cuts. arXiv preprint arXiv:2112.14488.
- Borchers, H. W. 2021. Numbers: Number-Theoretic Functions. R package version 0.8-2.
- Clare, A., J. W. Daykin, T. Mills, and C. Zarges. 2019. Evolutionary search techniques for the lyndon factorization of biosequences. In Proceedings of the Genetic and Evolutionary Computation Conference Companion, 1543–50. doi:10.1145/3319619.3326872.
- Compeau, P. E., P. A. Pevzner, and G. Tesler. 2011. Why are de Bruijn graphs useful for genome assembly? Nature Biotechnology 29 (11):987–91. doi:10.1038/nbt.2023.
- Crochemore, M., and D. Perrin. 1991. Two-way string-matching. Journal of the ACM 38 (3):650–74. doi:10.1145/116825.116845.
- De Felice, C., R. Zaccagnino, and R. Zizza. 2017. Unavoidable sets and circular splicing languages. Theoretical Computer Science 658:148–58. doi:10.1016/j.tcs.2016.09.008.
- Di Nardo, E. 2014. On a symbolic representation of non-central Wishart random matrices with applications. Journal of Multivariate Analysis 125:121–35. doi:10.1016/j.jmva.2013.12.001.
- Di Nardo, E., and G. Guarino. 2022. kstatistics: Unbiased estimates of joint cumulant products from the multivariate faà di bruno’s formula. The R Journal 14 (2):209–29. doi:10.32614/RJ-2022-033.
- Flajolet, P., and R. Sedgewick. 2009. Analytic combinatorics. New York, NY: Cambridge University Press.
- Fredricksen, H., and J. Maiorana. 1978. Necklaces of beads in k colors and k-ary de bruijn sequences. Discrete Mathematics 23 (3):207–10. doi:10.1016/0012-365X(78)90002-X.
- Frey, P. W., and L. R. Atkin. 1988. Creating a chess player. In Computer games I, 226–324. New York, NY.
- Harary, F. 1994. Pólya’s enumeration theorem. In Graph theory, 180–4. Reading. Massachusetts: Addison-Wesley.
- Kociumaka, T., J. Radoszewski, and W. Rytter. 2014. Computing k-th lyndon word and decoding lexicographically minimal de bruijn sequence. In Symposium on Combinatorial Pattern Matching, 202–11. Springer.
- Leiserson, C. E., H. Prokop, and K. H. Randall. 1998. Using de bruijn sequences to index a 1 in a computer word. Available on the Internet from 3 (5), http://supertech.csail.mit.edu/papers.html.
- Mallows, C., and L. Shepp. 2008. The necklace process. Journal of Applied Probability 45 (1):271–8. doi:10.1239/jap/1208358967.
- Di Nardo, E., and G. Guarino. 2013. A new algorithm for computing moments of complex non-central wishart distributions. Maple algorithm.
- Di Nardo, E., and G. Guarino. 2021. kStatistics: Unbiased Estimators for Cumulant Products and Faà Di Bruno’s Formula. R package version 2.1.
- Nica, A., and R. Speicher. 2006. Lectures on the combinatorics of free probability, volume 13. New York, NY: Cambridge University Press.
- Ralston, A. 1982. De bruijn sequences—a model example of the interaction of discrete mathematics and computer science. Mathematics Magazine 55 (3):131–43. doi:10.2307/2690079.
- Ruskey, F., and J. Sawada. 1999. An efficient algorithm for generating necklaces with fixed density. SIAM Journal on Computing 29 (2):671–84. doi:10.1137/S0097539798344112.
- Sawada, J., A. Williams, and D. Wong. 2016. Generalizing the classic greedy and necklace constructions of de Bruijn sequences and universal cycles. The Electronic Journal of Combinatorics 23 (1):1–24. doi:10.37236/5517.
- Schwartz, M., and T. Etzion. 1999. The structure of single-track gray codes. IEEE Transactions on Information Theory 45 (7):2383–96. doi:10.1109/18.796379.
- Tomohiro, I., Y. Nakashima, S. Inenaga, H. Bannai, and M. Takeda. 2013. Efficient lyndon factorization of grammar compressed text. In Combinatorial pattern matching, ed. J. Fischer and P. Sanders, 153–64. Berlin, Heidelberg: Springer.
- Vitkovskiy, A., P. Christodoulides, and V. Soteriou. 2012. A combinatorial application of necklaces: Modeling individual link failures in parallel network-on-chip interconnect links.