6533b85bfe1ef96bd12ba2bd
RESEARCH PRODUCT
A bijection between words and multisets of necklaces
Antonio RestivoChristophe ReutenauerIra M. Gesselsubject
Discrete mathematicsBurrows and Wheeler TransformMathematics::CombinatoricsSettore INF/01 - InformaticaFree Lie algebraLie superalgebrastandard permutationLexicographical orderTheoretical Computer ScienceImage (mathematics)CombinatoricsSet (abstract data type)PermutationComputational Theory and MathematicsBijectionDiscrete Mathematics and CombinatoricsGeometry and TopologyComputer Science::Formal Languages and Automata TheoryWord (group theory)MathematicsReal numberdescription
Two of the present authors have given in 1993 a bijection Phi between words on a totally ordered alphabet and multisets of primitive necklaces. At the same time and independently, Burrows and Wheeler gave a data compression algorithm which turns out to be a particular case of the inverse of Phi. In the present article, we show that if one replaces in Phi the standard permutation of a word by the co-standard one (reading the word from right to left), then the inverse bijection is computed using the alternate lexicographic order (which is the order of real numbers given by continued fractions) on necklaces, instead of the lexicographic order as for Phi(-1). The image of the new bijection, instead of being as for Phi the set of all multisets of primitive necklaces, is a special set of multisets of necklaces (not all primitive); it turns out that this set is naturally linked to the decomposition of the enveloping algebra of the oddly generated free Lie superalgebra, induced by the Poincare-Birkhoff-Witt theorem.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-10-01 |