Involution Solid and Join Codes

Involution Solid Codes

Insertion and Deletion for Involution Codes

This paper introduces a generalization of the operation of catenation: u[k]lv, the left-k-insertion, is the set of all words obtained by inserting v into u in positions that are at most k letters away from the left extremity of the word u. We define k-suffix codes using the left-kinsertion operation and extend the concept of k-prefix and k-suffix codes to involution k-prefix and involution k-su...

Minimal Bounded Lattices with an Antitone Involution the Complemented Elements of Which Do Not Form a Sublattice

Bounded lattices with an antitone involution the complemented elements of which do not form a sublattice must contain two complemented elements such that not both their join and their meet are complemented. We distinguish (up to symmetry) eight cases and in each of these cases we present such a lattice of minimal cardinality.

Enumerating spanning trees of graphs with an involution

As the extension of the previous work by Ciucu and the present authors (J. Combin. Theory Ser. A 112(2005) 105–116), this paper considers the problem of enumeration of spanning trees of weighted graphs with an involution which allows fixed points. We show that if G is a weighted graph with an involution, then the sum of weights of spanning trees of G can be expressed in terms of the product of ...

Ultra and Involution Ideals in $BCK$-algebras

In this paper, we define the notions of ultra and involution ideals in $BCK$-algebras. Then we get the relation among them and other ideals as (positive) implicative, associative, commutative and prime ideals. Specially, we show that in a bounded implicative $BCK$-algebra, any involution ideal is a positive implicative ideal and in a bounded positive implicative lower $BCK$-semilattice, the not...