In his study of a Hochschild complex arising in connection with the free loop fibration, S. Saneblidze defined freehedron, certain polytope constructed via truncation process from hypercube. It was recently conjectured by F. Chapoton and proven C. Combe that orientation 1-skeleton freehedron carries lattice structure. The resulting dubbed it is interval constructable extremal. These properties ...

In the paper Busaniche and Cignoli (2009) we presented a quasivariety of commutative residuated lattices, called NPc-lattices, that serves as an algebraic semantics for paraconsistent Nelson’s logic. In the present paper we show that NPc-lattices form a subvariety of the variety of commutative residuated lattices, we study congruences of NPc-lattices and some subvarieties of NPc-lattices.

Modular lattices, introduced by R. Dedekind, are an important subvariety of lattices that includes all distributive lattices. Heitzig and Reinhold [6] developed an algorithm to enumerate, up to isomorphism, all nite lattices up to size 18. Here we adapt and improve this algorithm to construct and count modular lattices up to size 23, semimodular lattices up to size 22, and lattices of size 19. ...

The commutative residuated lattices were first introduced by M. Ward and R.P. Dilworth as generalization of ideal lattices of rings. Non-commutative residuated lattices, called sometimes pseudo-residuated lattices, biresiduated lattices or generalized residuated lattices are algebraic counterpart of substructural logics, that is, logics which lack some of the three structural rules, namely cont...

in this note we are going to survey several invariants of finite groups related either to their orders or to generating sets or to lattices of subgroups. some relations among these invariants will be exhibited. special attention will be paid to monotonicity of them.

We study a class of lattices called weak* complemented lattices which are shown to have the property that the order complex of any interval of the lattice is either contractible or homotopy equivalent to a sphere. The two main examples are lattices generated by intervals in a total order and the lattices of partitions of integers under dominance order. The proofs are done mainly using homotopy ...