1,764 research outputs found
On Theta-palindromic Richness
In this paper we study generalization of the reversal mapping realized by an
arbitrary involutory antimorphism . It generalizes the notion of a
palindrome into a -palindrome -- a word invariant under . For
languages closed under we give the relation between
-palindromic complexity and factor complexity. We generalize the notion
of richness to -richness and we prove analogous characterizations of
words that are -rich, especially in the case of set of factors
invariant under . A criterion for -richness of
-episturmian words is given together with other examples of
-rich words.Comment: 14 page
Poly[aqua(μ3-pyridazine-4-carboxylato-κ2 O:O:O′)lithium]
The structure of the title compound, [Li(C5H3N2O2)(H2O)]n, is composed of centrosymmetric dimers in which two LiI ions are bridged by a carboxylate O atom, each donated by a ligand, acting in a bidentate mode. The second carboxylato O atoms bridge the dimers to LiI ions in adjacent dimers, forming molecular layers parallel to (001). Each LiI ion is coordinated by two bridging carboxylate O atoms, a bridging carboxylate O atom donated by the adjacent dimer and an aqua O atom, resulting in a distorted tetrahedral coordination geometry. The layers are held together by O—H⋯N hydrogen bonds in which coordinated water O atoms act as donors and ligand hetero-ring N atoms as acceptors
Generalized Thue-Morse words and palindromic richness
We prove that the generalized Thue-Morse word defined for
and as , where denotes the sum of digits in the base-
representation of the integer , has its language closed under all elements
of a group isomorphic to the dihedral group of order consisting of
morphisms and antimorphisms. Considering simultaneously antimorphisms , we show that is saturated by -palindromes
up to the highest possible level. Using the terminology generalizing the notion
of palindromic richness for more antimorphisms recently introduced by the
author and E. Pelantov\'a, we show that is -rich. We
also calculate the factor complexity of .Comment: 11 page
Poly[hydrazin-1-ium [diaquabis(μ4-pyridazine-3,6-dicarboxylato)trilithate] monohydrate]
The structure of the title compound, {(N2H5)[Li3(C6H2N2O4)2(H2O)2]·H2O}n, is composed of molecular dimers, each built up of two symmetry-related LiI ions with distorted trigonal–bipyramidal coordinations bridged by two deprotonated ligand molecules via their N,O-bonding sites. Doubly solvated LiI ions with a distorted tetrahedral geometry link adjacent dimers, forming a polymer generated by bridging bidentate carboxylato O atoms to LiI ions in adjacent dimers, forming anionic layers parallel to the ac plane with monoprotonated hydrazinium cations and crystal water molecules positioned between them. The layers are held together by an extended system of hydrogen bonds in which the hydrazinium cations and coordinated and crystal water molecules act as donors and carboxylate O atoms act as acceptors
Poly[di-μ2-aqua-μ2-(5-methylpyrazine-2-carboxylato)-(5-methylpyrazine-2-carboxylato)-μ3-nitrato-trilithium]
The asymmetric unit of the title compound, [Li3(C6H5N2O2)2(NO3)(H2O)2]n contains three LiI ions, two ligand anions, two water molecules and a nitrate anion. Related by a centre of inversion, they form a centrosymmetric molecular cluster in which one of the LiI ions shows trigonal–bipyramidal and the other two distorted tetrahedral coordination. LiI ions are bridged by water O atoms and carboxylate O atoms donated by one of the ligands. The clusters, bridged by two nitrato O atoms, form molecular columns along [010], which are held together by O—H⋯O and O—H⋯N hydrogen bonds and π–π interactions [centroid–centroid distances = 3.694 (1) and 3.796 (1) Å]
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