The classes of sequentially Cohen-Macaulay and sequentially homotopy Cohen-Macaulay complexes and posets are studied. First, some different versions of the definitions are discussed and the homotopy type is determined. Second, it is shown how various constructions, such as join, product and rank-selection preserve these properties. Third, a characterization of sequential Cohen-Macaulayness for ...

Given a graph G with p vertices, q edges and a positive integer k, a k-sequentially additive labeling of G is an assignment of distinct numbers k, k + 1, k + 2, . . . , k + p + q − 1 to the p + q elements of G so that every edge uv of G receives the sum of the numbers assigned to the vertices u and v. A graph which admits such an assignment to its elements is called a k-sequentially additive gr...

Let I ⊂ R be a graded ideal in the polynomial ring R = K[x1, . . . , xn] where K is a field, and fix a term order <. It has been shown in [17] that the Hilbert functions of the local cohomology modules of R/I are bounded by those of R/ in(I), where in(I) denotes the initial ideal of I with respect to <. In this note we study the question when the local cohomology modules of R/I and R/ in(I) hav...

A k-dissection D of a polygon P , is a partition of P into a set of subpolygons {Q1, . . . ,Qm} with disjoint interiors such that these can be reassembled to form k polygons P1, . . . ,Pk all similar to P . D is called non-trivial if none of {Q1, . . . ,Qm} is similar to P . In this paper we show that any convex n-gon has a k-dissection (resp. sequential dissection) with (k − 1)n + 1 pieces, n ...

When acting in a complex visual environment, it is essential to be able to flexibly allocate attention to parts of the visual scene that may contain goal-relevant information. The paper by Jia et al. provides novel evidence that our brains sequentially sample different objects in a visual scene. The results were obtained using "temporal response functions," in which unique electroencephalograph...

We prove that sequentially Cohen-Macaulay rings in positive characteristic, as well as sequentially Cohen-Macaulay Stanley-Reisner rings in any characteristic, have trivial Lyubeznik table. Some other configurations of Lyubeznik tables are also provided depending on the deficiency modules of the ring.

Let G be a simple (i.e., no loops and no multiple edges) graph. We investigate the question of how to modify G combinatorially to obtain a sequentially CohenMacaulay graph. We focus on modifications given by adding configurations of whiskers to G, where to add a whisker one adds a new vertex and an edge connecting this vertex to an existing vertex in G. We give various sufficient conditions and...

to be quasidiagonal when B⊗K contains an approximate unit of projections which is quasi-central in E, cf. [Sa]. He identified, under certain conditions, the subgroup of KK(A,B) which the quasidiagonal extensions correspond to under Kasparov’s isomorphism Ext(A,B) ' KK(A,B). C. Schochet has removed some of Salinas’ conditions in [S], the result being that when A is a unital C-algebra in the boot...

In plants whose flowers develop in a sequence, different flowers may exhibit temporal variation in pollen donation and receipt such that the fitness contributions through male and female functions can vary among flowers. Dichogamy, or directional pollinator movements within inflorescences, can create situations where flowers in different stages in the sequence may differ in the numbers of flowe...

Recently, distributed shared memory (DSM) systems have received much attention because such an abstraction simpliies programming. An important class of DSM implementations is one which uses cache memories to improve eeciency. In this paper, we present a cache-consistency protocol for DSM which requires signiicantly less communication than previously proposed protocols. This is achieved by maint...