arXiv subjects

Stephen M. Buckley

Publications and source records attributed to Stephen M. Buckley.

6 recordsLinked to original sources

arXiv2025

Wiring switches to more light bulbs

Given $n$ buttons and $n$ bulbs so that the $i$th button toggles the $i$th bulb and perhaps some other bulbs, we compute the sharp lower bound on the number of bulbs that can be lit regardless of the action of the buttons. In the previous article we dealt with the case where each button affects at most 2 or 3 bulbs. In the present article we give sharp lower bounds for up to 4 or 5 wires per switch, and we show that the sharp asymptotic bound for an arbitrary number of wires is $\frac12$. (Even if you've found their buttons, you can please no more than half the people all the time!)

math.CO↗

arXiv2024

Wiring Switches to Light Bulbs

Given n buttons and n bulbs so that the ith button toggles the ith bulb and at most two other bulbs, we compute the sharp lower bound on the number of bulbs that can be lit regardless of the action of the buttons.

math.CO↗

arXiv2013

The Boundary at Infinity of a rough CAT(0) space

We develop the boundary theory of rough CAT(0) spaces, a class of spaces that contains both Gromov hyperbolic and CAT(0) spaces. The resulting theory generalizes the common features of the Gromov boundary of a Gromov hyperbolic space and the ideal boundary of a complete CAT(0) space. It is not assumed that the spaces are geodesic or proper.

math.MG↗

arXiv2013

Natural maps between CAT(0) boundaries

It is shown that certain natural maps between the ideal, Gromov, and end boundaries of a complete CAT(0) space can fail to be either injective or surjective. Additionally the natural map from the Gromov boundary to the end boundary of a complete CAT(-1) space can fail to be either injective or surjective.

math.MG↗

arXiv2012

Distinguishing properties of weak slice conditions II

The slice condition and the more general weak slice conditions are geometric conditions on Euclidean space domains which have evolved over the last several years as a tool in various areas of analysis. This paper examines some of their finer distinctive properties.

math.MG↗

arXiv2011

Rough CAT(0) spaces

We investigate various notions of rough CAT(0). These conditions define classes of spaces that strictly include the union of all Gromov hyperbolic length spaces and all CAT(0) spaces.

math.MG↗