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Consider a random word $X^n=(X_1,\ldots ,X_n)$ in an alphabet consisting of $4$ letters, with the letters viewed either as $A$, $U$, $G$ and $C$ (i.e., nucleotides in an RNA sequence) or $\alpha$, $\bar{\alpha}$, $\beta$ and $\bar{\beta}$ (i.e., gene
Externí odkaz:
http://arxiv.org/abs/2007.12109
Autor:
Gadgil, Siddhartha
We describe a case of an interplay between human and computer proving which played a role in the discovery of an interesting mathematical result. The unusual feature of the use of computers here was that a computer generated but human readable proof
Externí odkaz:
http://arxiv.org/abs/1904.05214
Autor:
Polymath, D. H. J.
Publikováno v:
Alg. Number Th. 12 (2018) 1773-1786
A pseudo-length function defined on an arbitrary group $G = (G,\cdot,e, (\,)^{-1})$ is a map $\ell: G \to [0,+\infty)$ obeying $\ell(e)=0$, the symmetry property $\ell(x^{-1}) = \ell(x)$, and the triangle inequality $\ell(xy) \leqslant \ell(x) + \ell
Externí odkaz:
http://arxiv.org/abs/1801.03908
Autor:
Duncan, Andrew, Fulthorp, Steven
In 1962 M.J. Wicks gave a precise description of the form a commutator could take in a free group or a free product and in 1973 extended this description to cover a product of two squares. Subsequently, lists of "Wicks forms" were found for arbitrary
Externí odkaz:
http://arxiv.org/abs/1509.01308
Autor:
Calegari, Danny, Zhuang, Dongping
Publikováno v:
Contemp. Math. 560 (2011), 145-169
We study stable W-length in groups, especially for W equal to the n-fold commutator gamma_n:=[x_1,[x_2, . . . [x_{n-1},x_n]] . . . ]. We prove that in any perfect group, for any n at least 2 and any element g, the stable commutator length of g is at
Externí odkaz:
http://arxiv.org/abs/1008.2219
Publikováno v:
Indian Journal of Pure and Applied Mathematics.
Consider a random word $X^n=(X_1,\ldots ,X_n)$ in an alphabet consisting of $4$ letters, with the letters viewed either as $A$, $U$, $G$ and $C$ (i.e., nucleotides in an RNA sequence) or $\alpha$, $\bar{\alpha}$, $\beta$ and $\bar{\beta}$ (i.e., gene
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::765de658baf1fe6b4b5e9decfdd5a02c
https://doi.org/10.1007/s13226-022-00240-x
https://doi.org/10.1007/s13226-022-00240-x
Publikováno v:
Algebra Number Theory 12, no. 7 (2018), 1773-1786
A pseudo-length function defined on an arbitrary group $G = (G,\cdot,e, (\,)^{-1})$ is a map $\ell: G \to [0,+\infty)$ obeying $\ell(e)=0$, the symmetry property $\ell(x^{-1}) = \ell(x)$, and the triangle inequality $\ell(xy) \leqslant \ell(x) + \ell
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::08a5e9bb869b1d876daca6a3282b4111
https://projecteuclid.org/euclid.ant/1541732441
https://projecteuclid.org/euclid.ant/1541732441
Autor:
Calegari, Danny, Zhuang, Dongping
We study stable W-length in groups, especially for W equal to the n-fold commutator gamma_n:=[x_1,[x_2, . . . [x_{n-1},x_n]] . . . ]. We prove that in any perfect group, for any n at least 2 and any element g, the stable commutator length of g is at
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8726bab9bf6afe55ad3e9319f5f8fad1
https://resolver.caltech.edu/CaltechAUTHORS:20120319-082257258
https://resolver.caltech.edu/CaltechAUTHORS:20120319-082257258