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   Associative string functions; Marichal, Jean-Luc  ; Teheux, Bruno in Asian-European Journal of Mathematics (2014), 7(4), 145005918 We introduce the concept of associativity for string functions, where a string function is a unary operation on the set of strings over a given alphabet. We discuss this new property and describe certain ... [more ▼] We introduce the concept of associativity for string functions, where a string function is a unary operation on the set of strings over a given alphabet. We discuss this new property and describe certain classes of associative string functions. We also characterize the recently introduced preassociative functions as compositions of associative string functions with injective unary maps. Finally, we provide descriptions of the classes of associative and preassociative functions which depend only on the length of the input. [less ▲] Detailed reference viewed: 161 (30 UL)Intervals of the homomorphism order of graphs have infinite width; Schölzel, Karsten E-print/Working paper (2014) The homomorphism order of graphs is known to be dense with a single exception. We strengthen this result by showing that, with this single exception, the interval between any two distinct comparable ... [more ▼] The homomorphism order of graphs is known to be dense with a single exception. We strengthen this result by showing that, with this single exception, the interval between any two distinct comparable graphs includes an infinite antichain. Moreover, every antichain included in such an interval can be extended into an infinite one within that interval. [less ▲] Detailed reference viewed: 42 (3 UL) |
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