A frame in an n-dimensional Hilbert space Hn is a possibly redundant collection of vectors {fi}i∈I that span the space. A tight frame is a generalization of an orthonormal basis. A frame {fi}i∈I is said to be scalable if there exist nonnegative scalars {ci}i∈I such that {cifi}i∈I is a tight frame. In this paper we study the combinatorial structure of frames and their decomposition into tight or...

Homotopy type of partially ordered sets (poset for short) play a crucial role in algebraic topology. In fact, every space is weakly equivalent to a simplicial complex which, of course, can be considered as a poset. Posets also arise in more specific contexts as homological decompositions [10, 6, 16, 20] and subgroups complexes associated to finite groups [7, 26, 4]. The easy structure of a pose...

We prove that every height-2 finite poset with three or more points has an incomparable pair (.x, J) such that the proportion of all linear extensions of the poset in which s is less than y is between l/3 and 213. A related result of Koml6s says that the containment interval [l/3,2/3] shrinks to [l/2, l/2] in the limit as the width of height-2 posets becomes large. We conjecture that a poset de...

The consecutive pattern poset is the infinite partially ordered set of all permutations where σ ≤ τ if τ has a subsequence of adjacent entries in the same relative order as the entries of σ. We study the structure of the intervals in this poset from topological, poset-theoretic, and enumerative perspectives. In particular, we prove that all intervals are rank-unimodal and strongly Sperner, and ...

It is known that being hierarchical is a necessary and sufficient condition for a poset to admit MacWilliams identity. In this paper, we completely characterize the structures of posets which have an association scheme structure whose relations are indexed by the poset distance between the points in the space. We also derive an explicit formula for the eigenmatrices of association schemes induc...

Families of maps on the lattice of all antichains of a finite bounded poset that extend the blocker, deletion, and contraction maps on clutters are considered. Influence of the parameters of the maps is investigated. Order-theoretic extensions of some principal relations for the set-theoretic blocker, deletion, and contraction maps on clutters are presented. 1. Introduction and preliminary. Let...

In this paper, we describe and discuss a DOS based POset (i.e. Partially Ordered Set) implementation. We begin with a short review of previous results on POset based protection. We then describe implementation details of POset based protection under DOS. Next we discuss management tools used to implement and control the protection system. Then we describe the problems encountered in integration...

In this paper, we formally define a useful data structure for content-based routing and event delivery. The poset (partially ordered set)-derived forest data structure is induced by the partial order created by the covering relation between event filters. Two extensions of the basic data structure are discussed: colored forests and the weakly merging forest. We give performance figures for the ...

It is shown that the Boolean center of complemented elements in a bounded integral residuated lattice characterizes direct decompositions. Generalizing both Boolean products and poset sums of residuated lattices, the concepts of poset product, Priestley product and Esakia product of algebras are defined and used to prove decomposition theorems for various ordered algebras. In particular, we sho...

Anders Björner characterized which finite graded partially ordered sets arise as the closure relation on cells of a finite regular CW complex. His characterization of these “CW posets” required each open interval (0̂, u) to have order complex homeomorphic to a sphere of dimension rk(u)− 2. Work of Danaraj and Klee showed that sufficient conditions were for the poset to be thin and shellable. The...