A holistic aboriginal framework for individual healing

This paper offers up an holistic Indigenous model of individual healing that utilizes medicine wheel teachings to break down the four aspects (spiritual, emotional, physical, and mental) of individual wellness. Teachings about each direction are presented followed by practice techniques for each aspect of the individual self. It is bookended by an introduction to the historical trauma faced by Indigenous peoples in Canada, and a conclusion that draws implications for healing

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

Integrable systems from the classical reflection equation

We construct integrable Hamiltonian systems on $G/K$, where $G$ is a quasitriangular Poisson Lie group and $K$ is a Lie subgroup arising as the fixed point set of a group automorphism $\sigma$ of $G$ satisfying the classical reflection equation. In the case that $G$ is factorizable, we show that the time evolution of these systems is described by a Lax equation, and present its solution in terms of a factorization problem in $G$. Our construction is closely related to the semiclassical limit of Sklyanin's integrable quantum spin chains with reflecting boundaries.Comment: 23 pages, published versio