Computer-generated symmetric chain decompositions for L(4,n) and L(3,n)

Symmetric Chain Decompositions of Linear Lattices

Venn Diagrams and Symmetric Chain Decompositions in the Boolean Lattice

We show that symmetric Venn diagrams for n sets exist for every prime n, settling an open question. Until this time, n = 11 was the largest prime for which the existence of such diagrams had been proven, a result of Peter Hamburger. We show that the problem can be reduced to finding a symmetric chain decomposition, satisfying a certain cover property, in a subposet of the Boolean lattice Bn, an...

Symmetric Chain Decompositions of Quotients by Wreath Products

Subgroups of the symmetric group Sn act on C n (the n-fold product C×· · ·×C of a chain C) by permuting coordinates, and induce automorphisms of the power Cn. For certain families of subgroups of Sn, the quotients defined by these groups can be shown to have symmetric chain decompositions (SCDs). These SCDs allow us to enlarge the collection of subgroups G of Sn for which the quotient 2 n/G on ...

Symmetric Chain Decompositions of Quotients of Chain Products by Wreath Products

Subgroups of the symmetric group Sn act on powers of chains C n by permuting coordinates, and induce automorphisms of the ordered sets C. The quotients defined are candidates for symmetric chain decompositions. We establish this for some families of groups in order to enlarge the collection of subgroups G of the symmetric group Sn for which the quotient Bn/G obtained from the G-orbits on the Bo...

Tangential Frequency Ltering Decompositions for Symmetric Matrices

The tangential frequency ltering decomposition (TFFD) is introduced. The convergence theory of an iterative scheme based on the TFFD for symmetric matrices is the focus of this paper. The existence of the TFFD and the convergence of the induced iterative algorithm is shown for symmetric and positive deenite matrices. Convergence rates independent of the number of unknowns are proven for a small...