5,056 research outputs found
A partition of connected graphs
We define an algorithm k which takes a connected graph G on a totally ordered
vertex set and returns an increasing tree R (which is not necessarily a subtree
of G). We characterize the set of graphs G such that k(G)=R. Because this set
has a simple structure (it is isomorphic to a product of non-empty power sets),
it is easy to evaluate certain graph invariants in terms of increasing trees.
In particular, we prove that, up to sign, the coefficient of x^q in the
chromatic polynomial of G is the number of increasing forests with q components
that satisfy a condition that we call G-connectedness. We also find a bijection
between increasing G-connected trees and broken circuit free subtrees of G.Comment: 8 page
Enumeration of paths and cycles and e-coefficients of incomparability graphs
We prove that the number of Hamiltonian paths on the complement of an acyclic
digraph is equal to the number of cycle covers. As an application, we obtain a
new expansion of the chromatic symmetric function of incomparability graphs in
terms of elementary symmetric functions. Analysis of some of the combinatorial
implications of this expansion leads to three bijections involving acyclic
orientations
In The Trenches: Traditional Healers\u27 Understanding of Health and Healing
This study explored understandings of traditional healing from the perspectives of traditional healers and helpers. The sample of sixteen individuals was initially identified by key informants, and then the sample snowballed by word of mouth. Among the sample are healers from a variety of cultures, including Anishnaabe, Mohawk, Oneida, Seneca, Paiute, Inuit, Innu, and Potawatomi. Traditional Indigenous protocols were followed by the researcher during the course of the study. In-depth interviews were conducted with each participant. Interviews were audio-recorded and verbatim transcripts were analyzed qualitatively. These individuals shared their understanding of the work that they do, including ceremonies, use of medicine, power of prayer, and rites of passage, as well as the implications of traditional healing in this ever-changing society. The findings suggest there is a growing need for traditional healing with Indigenous people
Set maps, umbral calculus, and the chromatic polynomial
Some important properties of the chromatic polynomial also hold for any
polynomial set map satisfying p_S(x+y)=\sum_{T\uplus U=S}p_T(x)p_U(y). Using
umbral calculus, we give a formula for the expansion of such a set map in terms
of any polynomial sequence of binomial type. This leads to some new expansions
of the chromatic polynomial. We also describe a set map generalization of Abel
polynomials.Comment: 20 page
Current Status of VHE Astronomy
Very-high-energy astronomy studies the Universe at energies between 30 GeV
and 100 TeV. The past decade has seen enormous progress in this field. There
are now at least seven known sources of VHE photons. By studying these objects
in the VHE regime one can begin to understand the environments surrounding
these objects, and how particle acceleration is realized in nature. In addition
the photon beams from the extragalactic gamma-ray sources can be used to study
the electromagnetic fields in the intervening space. This recent progress can
be traced to the development of a new class of detector with the ability to
differentiate between air showers produced by gamma rays and those produced by
the much more numerous hadronic cosmic-ray background. Much more sensitive
instruments are currently in the design phase and two new types of instruments
are beginning to take data. In this paper we will discuss the physics of these
sources and describe the existing and planned detectors.Comment: 7 pages, 3 figure
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