Combinatorics on Words

By Tero Harju. 2004

1,302 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/306ac32ccc987e65ac669fd6c793e9bee89ccf61

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Citations in the corpus

Grobner-Shirshov Bases for Associative Algebras with Multiple Operators and Free Rota-Baxter Algebras ∗† (2008, background): “([9], 1954), and independently to Shirshov ([7], 1958)) play a significant role in algebra and combinatorics (see, for example, [10–15]; they are often called Lyndon basis and Lyndon words, see, for example, [14,15]).”
Combinatorial algebra : syntax and semantics (2014, neutral): “More on avoidable words, Prouhet–Morse–Thue words and related topics, applications to dynamics and arithmetics can be found in the books by Lothaire [206, 207] and N.”
Theory and Applications of Models of Computation: 15th Annual Conference, TAMC 2019, Kitakyushu, Japan, April 13–16, 2019, Proceedings (2019, methodology): “Therefore, we can make use of some known results about the sink problem on path networks [3,7].”
Construction of Sturmian sequences (2005, methodology): “Given an inﬁnite sequence F , its language complexity p(n, F) is deﬁned to be the number of its factors of length n , which has been extensively studied in the last few years, e.g. [21].”
NEW IDENTITIES IN DENDRIFORM ALGEBRAS (2007, background): “A fundamental theorem [Lot83] asserts that each word w in X has a unique Lyndon factorisation, i.”
Representations of Khovanov–Lauda–Rouquier algebras and combinatorics of Lyndon words (2009, neutral): “It is well known [15, 18] that every word i has a unique factorization i = i((1))i((2)) · · · i such that i((1)) ≥ i((2)) ≥ · · · ≥ i are Lyndon words.”
Analytic Combinatorics (2009, background): “Our treatment of words and languages largely draws its inspiration from th e line of research started by Scḧ utzenberger in the early 1960s and on the subsequent account to be fo und in Lothaire’s book [413].”
A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems (2010, background): “The Shirshov decomposition of u is the decomposition u = vw, with v, w ∈ L such that w is the smallest end among those proper non-empty ends of u, see [Lo].”
A combinatorial property and power graphs of semigroups (2004, neutral): “Keywords: sequences, power graphs, semigroups Classification: 5C20, 05C25, 05C50”
Dynamical properties of the negative beta-transformation (2011, positive): “Here, φ is a morphism on finite words on the alphabet {1, 2}, which is naturally extended to the set of infinite words {1, 2}N, as in [15], and limβ→1 d−β(1)= u means that longer and longer prefixes of d−β(1) agree with prefixes of u when β→ 1.”
Gröbner–Shirshov bases and their calculation (2013, background): “Actually, he cites [72] by mistake, as that result is absent from the paper, see Berstel and Perrin [12].8 Starting with the book of Lothaire, Combinatorics on words ([151], 1983), some authors called the words and basis ‘Lyndon words’ and ‘Lyndon basis’; for instance, see Reutenauer, Free Lie algeb”