Morgenstern ([Mor95]) claimed to have constructed fundamental domains for congruence subgroups of the lattice group Γ = PGL2(Fq[t]), and subgraphs providing the first known examples of linear families of bounded concentrators. His method was to construct the fundamental domain for a congruence subgroup as a ‘ramified covering’ of the fundamental domain for Γ on the Bruhat-Tits tree X = Xq+1 of ...

We prove the equivalence of EL-shellability and existence recursive atom ordering independent roots. show that a comodernistic lattice, as defined by Schweig Woodroofe, admits roots, therefore is EL-shellable. also present discuss simpler EL-shelling on one most important classes order congruence lattices.

Let L → H be a lattice homomorphism and let a “readable” drawing of H be given. It is natural to make use of it to try getting a clear(er) drawing of L. Hence, the following question is explored: How the knowledge of the congruence lattice Con(L) of L can help in getting “better” drawings of L? This will be done by proposing rank shelling procedures of (M(Con(L),≤) and will be illustrated with ...

We denote by Conc L the (∨, 0)-semilattice of all finitely generated congruences of a lattice L. For varieties (i.e., equational classes) V and W of lattices such that V is contained neither in W nor in its dual, and such that every simple member of W contains a prime interval, we prove that there exists a bounded lattice A ∈ V with at most א2 elements such that Conc A is not isomorphic to Conc...

This work investigates the factorization of finite lattices to implode selected intervals while preserving remaining order structure. We examine how complete congruence relations and tolerance can be utilized for this purpose answer question finding finest those a given interval in generated factor lattice. To overcome limitations based on relations, we introduce new lattice that enables implod...

Chi calculus was proposed as a process calculus that has a uniform treatment of names. Preliminary properties of chi calculus have been examined in literature. In this paper a more systematic study of bisimilarities for chi processes is carried out. The notion of L-bisimilarity is introduced to give a possible classification of bisimilarities on chi processes. It is shown that the set of L-bisi...

One of the most fruitful results from Minkowski’s geometric viewpoint on number theory is his so called 1st Fundamental Theorem. It provides an optimal upper bound for the volume of an o-symmetric convex body whose only interior lattice point is the origin. Minkowski also obtained a discrete analog by proving optimal upper bounds on the number of lattice points in the boundary of such convex bo...

Let L be a bounded distributive lattice. For k 1, let Sk (L) be the lattice of k-ary functions on L with the congruence substitution property (Boolean functions); let S(L) be the lattice of all Boolean functions. The lattices that can arise as Sk (L) or S(L) for some bounded distributive lattice L are characterized in terms of their Priestley spaces of prime ideals. For bounded distributive lat...