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pro vyhledávání: '"Zimin, A. A."'
Zimin words are words that have the same prefix and suffix. They are unavoidable patterns, with all sufficiently large strings encompassing them. Here, we examine for the first time the presence of k-mers not containing any Zimin patterns, defined he
Externí odkaz:
http://arxiv.org/abs/2410.13004
Autor:
Carayol, Arnaud, Göller, Stefan
A pattern is encountered in a word if some infix of the word is the image of the pattern under some non-erasing morphism. A pattern $p$ is unavoidable if, over every finite alphabet, every sufficiently long word encounters $p$. A theorem by Zimin and
Externí odkaz:
http://arxiv.org/abs/1902.05540
Autor:
Connor, John
This paper gives a short overview of Zimin words, and proves an interesting property of their distribution. Let $L_q^m$ to be the lexically ordered sequence of $q$-ary words of length $m$, and let $T_n(L_q^m)$ to be the binary sequence where the $i$-
Externí odkaz:
http://arxiv.org/abs/1611.01061
We present an all-optical concept for measuring the electric field of light spanning from infrared to extreme ultraviolet with multi-petahertz detection bandwidth. Our approach employs a heterodyne detection of light produced by a highly nonlinear li
Externí odkaz:
http://arxiv.org/abs/2410.19196
We give an explicit counterexample to the Bunkbed Conjecture introduced by Kasteleyn in 1985. The counterexample is given by a planar graph on $7222$ vertices, and is built on the recent work of Hollom (2024).
Comment: 12 pages, 2 figures
Comment: 12 pages, 2 figures
Externí odkaz:
http://arxiv.org/abs/2410.02545
Autor:
Cooper, Joshua, Rorabaugh, Danny
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol. 18 no. 3, Combinatorics (March 17, 2016) dmtcs:1302
Word $W$ is an instance of word $V$ provided there is a homomorphism $\phi$ mapping letters to nonempty words so that $\phi(V) = W$. For example, taking $\phi$ such that $\phi(c)=fr$, $\phi(o)=e$ and $\phi(l)=zer$, we see that "freezer" is an instanc
Externí odkaz:
http://arxiv.org/abs/1510.03917
Autor:
Rytter, Wojciech, Shur, Arseny M.
Publikováno v:
Theoretical Computer Science, Vol. 571 (2015), 50-57
In the area of pattern avoidability the central role is played by special words called Zimin patterns. The symbols of these patterns are treated as variables and the rank of the pattern is its number of variables. Zimin type of a word $x$ is introduc
Externí odkaz:
http://arxiv.org/abs/1409.8235
Autor:
Cooper, Joshua, Rorabaugh, Danny
How long can a word be that avoids the unavoidable? Word $W$ encounters word $V$ provided there is a homomorphism $\phi$ defined by mapping letters to nonempty words such that $\phi(V)$ is a subword of $W$. Otherwise, $W$ is said to avoid $V$. If, on
Externí odkaz:
http://arxiv.org/abs/1409.3080
Autor:
Głowinski, Radosław, Rytter, Wojciech
Zimin words are very special finite words which are closely related to the pattern-avoidability problem. This problem consists in testing if an instance of a given pattern with variables occurs in almost all words over any finite alphabet. The proble
Externí odkaz:
http://arxiv.org/abs/1307.1560
Autor:
Wang, Zilong, Cui, Yuedong, Zhong, Li, Zhang, Zimin, Yin, Da, Lin, Bill Yuchen, Shang, Jingbo
Office automation significantly enhances human productivity by automatically finishing routine tasks in the workflow. Beyond the basic information extraction studied in much of the prior document AI literature, the office automation research should b
Externí odkaz:
http://arxiv.org/abs/2407.19056