Ramsey Goodness and Beyond

In a seminal paper from 1983, Burr and Erdos started the systematic study of Ramsey numbers of cliques vs. large sparse graphs, raising a number of problems. In this paper we develop a new approach to such Ramsey problems using a mix of the Szemeredi regularity lemma, embedding of sparse graphs, Turan type stability, and other structural results. We give exact Ramsey numbers for various classes of graphs, solving all but one of the Burr-Erdos problems.Comment: A new reference is adde

Facts, Values and Quanta

Quantum mechanics is a fundamentally probabilistic theory (at least so far as the empirical predictions are concerned). It follows that, if one wants to properly understand quantum mechanics, it is essential to clearly understand the meaning of probability statements. The interpretation of probability has excited nearly as much philosophical controversy as the interpretation of quantum mechanics. 20th century physicists have mostly adopted a frequentist conception. In this paper it is argued that we ought, instead, to adopt a logical or Bayesian conception. The paper includes a comparison of the orthodox and Bayesian theories of statistical inference. It concludes with a few remarks concerning the implications for the concept of physical reality.Comment: 30 pages, AMS Late

Packing Plane Spanning Trees and Paths in Complete Geometric Graphs

We consider the following question: How many edge-disjoint plane spanning trees are contained in a complete geometric graph $GK_n$ on any set $S$ of $n$ points in general position in the plane? We show that this number is in $\Omega(\sqrt{n})$. Further, we consider variants of this problem by bounding the diameter and the degree of the trees (in particular considering spanning paths).Comment: This work was presented at the 26th Canadian Conference on Computational Geometry (CCCG 2014), Halifax, Nova Scotia, Canada, 2014. The journal version appeared in Information Processing Letters, 124 (2017), 35--4

Signifier of Kiwi Identity

Contested myths of origin surround one of New Zealand’s best-loved cultural icons, or ‘kiwiana’: a pull-along children’s toy called the Buzzy Bee. This paper clarifies those domains by presenting new information gleaned from Betty Schlesinger, widow of the bee’s inventor. Clarification is important because the Buzzy Bee is, as kiwiana, a material item strongly associated with Kiwi identity. As a Māori word, ‘Kiwi’ is a common, often self-ascribed, term identifying people from Aotearoa New Zealand. In clarifying the Buzzy Bee’s history, this paper adds new information to the knowledge base of what it means to be Kiwi. That knowledge base is enhanced, because this paper notes that the Buzzy Bee was invented and first manufactured here in New Zealand by Betty Schlesinger’s husband Maurice Schlesinger. Betty Schlesinger’s account contrasts more popular and well-known origin myths that have served to cloud the Bee’s definitive history. In clarifying the Buzzy Bee’s genesis using Betty Schlesinger’s narrative, this paper also emphasises the important link between identity, materiality and national identity

THE ELECTRONIC JOURNAL OF COMBINATORICS (2014), DS1.14 References

and Computing 11. The results of 143 references depend on computer algorithms. The references are ordered alphabetically by the last name of the first author, and where multiple papers have the same first author they are ordered by the last name of the second author, etc. We preferred that all work by the same author be in consecutive positions. Unfortunately, this causes that some of the abbreviations are not in alphabetical order. For example, [BaRT] is earlier on the list than [BaLS]. We also wish to explain a possible confusion with respect to the order of parts and spelling of Chinese names. We put them without any abbreviations, often with the last name written first as is customary in original. Sometimes this is different from the citations in other sources. One can obtain all variations of writing any specific name by consulting the authors database of Mathematical Reviews a

Charles Willson Peale’s The Exhumation of the Mastodon and the Great Chain of Being: The Interaction of Religion, Science, and Art in Early-Federal America

In this paper, I explore Peale’s monumental painting, a work that is many things, a self-portrait and history painting among others. Indeed, in this painting, Peale was responding to science, religion, and their shifting positions within early-nineteenth-century America. When viewed together, Peale’s The Exhumation of the Mastodon is not merely a record of an event that occurred in New York during the early nineteenth century, and instead is a document of Peale and the interaction of science and religion in early-Federal America