Algebraic Combinatorics on Words

By J. Allouche. 2005

1,101 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/c3d3aee8dc0bb9a78e95106e44422f71ffc38274

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In Computational Theory and Mathematics

Citations in the corpus

Minimal varieties of residuated lattices (2005, background): “For a more precise definition of the lower mechanical word associated with a line and for the proofs of the facts mentioned above, the reader is referred to [14].”
Algebraic and combinatorial structures on pairs of twin binary trees (2012, background): “…on words leading to the deﬁnition of monoids on combinatorial objects Indeed, FSym is directly obtained from the plactic monoid [LS81,DHT02, Lot02], Bell from the Bell monoid [Rey07], PBT from the sylvester monoid [HNT02,HNT05], and Sym from the hypoplactic monoid [KT97,Nov98] The richness…”
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”
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.”
Combinatorics on Words (2004, background): “Sturmian words have many characterizations, see [12].”
Powers of rationals modulo 1 and rational base number systems (2008, methodology): “The properties of the β-shift are well understood, using the so-called “β-expansion of 1”, see [18, 14].”
On the Pisot Substitution Conjecture (2015, background): “For more detail, the reader is referred to [85].”
A New Generalization of Fibonacci Sequence & Extended Binet's Formula (2009, neutral): “Then for n ≥ 1, each sn is a prefix of ω(α) and ω(α) = lim n→∞ sn (again see [23]).”
Codimensions of algebras and growth functions (2008, methodology): “Moreover, it is known that Compw(n) n + 1 for any aperiodic word and an infinite word w is called a Sturmian word if Compw(n) = n + 1 for all n 1 (see [12]).”
Strictly Ergodic Subshifts and Associated Operators (2005, neutral): “For the proofs omitted in this subsection and much more information on Sturmian sequences and subshifts, we refer the reader to [16, 44, 113, 117].”