Search

We investigate symbolic and regular powers of monomial ideals. For a square-free monomial ideal $I$ in $k[x_0, \ldots, x_n]$ we show $I^{t(m+e-1)-e+r)}$ is a subset of $M^{(t-1)(e-1)+r-1}(I^{(m)})^t$ for all positive integers $m$, $t$ and $r$, where $e$ is the big-height of $I$ and $M = (x_0, \ldots, x_n)$. This captures two conjectures ($r=1$ and $r=e$): one of Harbourne-Huneke and one of Bocci-Cooper-Harbourne. We also introduce the symbolic polyhedron of a monomial ideal and use this to explore symbolic powers of non-square-free monomial ideals., 15 pages. Fixed typo

The significant impact of extant carnivores, particularly spotted hyenas, on the depositional history and physical characteristics of archaeofaunal and paleontological assemblages is well recognized. We focus on the behavioral ecology of extant spotted hyenas (Crocuta crocuta) in relation to bone accumulations produced by one East African clan at communal dens. Limbs and skulls of prey animals more frequently appear at dens than do other carcass portions. These items reflect the relative abundance of prey species near dens; carnivore remains are poorly represented. Comparative analysis reveals that bones are deposited far more slowly (Crocutadens than at dens of either brown (Parahyaena brunnea) or striped (Hyaena hyaena) hyenas. We propose that extantCrocutabone accumulation rates and sizes are likely affected by prey species abundance, clan size, social interactions within the clan, and the type and availability of den sites. We also suggest that the potential for intraspecific behavioral variability in bone accumulation patterns is important when comparisons are made among spotted hyena populations and across hyena species. For example, accumulation patterns may be dramatically influenced by the temporal span, potentially ranging from days to hundreds or thousands of years, in which bones are collected, depending on the species-specific history of occupation at a given site. Understanding the behavioral and ecological variability likely to influence bone accumulation patterns at dens used by different hyaenids will allow taphonomists and zooarchaeologists to refine their knowledge of mechanisms underlying site formation processes and potential causes of variability in deeper-time den assemblages.