We study the problem of computing the minimal number of adjacent, non-intersecting block interchanges required to transform a permutation into the identity permutation. In particular, we use the graph of a permutation to compute that number for a particular class of permutations in linear time and space, and derive a new tight upper bound on the so-called transposition distance.

Let L denote the free Lie ring of rank 2r with free generators xi , yi (1 i r), and let τ be the automorphism of L that interchanges xi and yi for all i . We construct a Z-basis of L that consists of pairs of elements which are interchanged by τ , and elements upon which τ acts as multiplication by −1.

We construct a uniform model for highest weight crystals and $B(\infty)$ generalized Kac--Moody algebras using rigged configurations. also show an explicit description of the $\ast$-involution on configurations $B(\infty)$: that interchanges rigging corigging. do this by giving recognition theorem $\ast$-involution. As consequence, we characterize $B(\lambda)$ as subcrystal

a series of amino derivative of 1-indene and 9-fluorene have been synthesized from their corresponding iminium salt, generated in situ in the concentrated ethereal lithium perchlorate solution, and 1-indenyl or 9-fluorenyl anions. the yields of the reactions depend on the kind of anion. addition of 1-indeny anion to the iminium salt gives the amino derivative of 1-indene, while addition of fluo...

We address the problem of finding the minimal number of block interchanges (exchange of two intervals) required to transform a duplicated linear genome into a tandem duplicated linear genome. We provide a formula for the distance as well as a polynomial time algorithm for the sorting problem.

A constraint satisfaction problem is a permutation problem if it has the same number of values as variables, all variables have the same domain and any solution assigns a permutation of the values to the variables. The dual CSP interchanges the variables and values; the eeects of combining both sets of variables in a single CSP are discussed.

It is shown that in the variety of orthomodular lattices every hypersubstitution respecting all absorption laws either leaves the lattice operations unchanged or interchanges join and meet. Further, in a variety of lattices with an involutory antiautomorphism a semigroup generated by three involutory hypersubstitutions is described.

It is shown that the T-duality in σ-model with Kaluza-Klein metric, without or with a torsion term, can be interpreted as electric-magnetic duality for some of their solitonic solutions. Actually Buscher’s duality transformation interchanges the topological and Noether charges. ∗E-mail: tabriz [email protected]

Results of density functional theory calculations on possible mechanisms for formation of the diterpenoid cyclooctatin are described. These results are consistent with the involvement of an unexpected 1,3-alkyl shift that interconverts two cyclopropylcarbinyl carbocations and interchanges the positions of two carbon atoms in an 8-membered ring. Predictions for future experiments to provide furt...

We address the problem of finding the minimal number of block interchanges (exchange of two intervals) required to transform a duplicated linear genome into a tandem duplicated linear genome. We provide a formula for the distance as well as a polynomial time algorithm for the sorting problem.