Related papers: Solitaire: Recent Developments
Cages ($r$-regular graphs of girth $g$ and minimum order) and their variants have been studied for over seventy years. Here we propose a new variant, "weighted cages". We characterize their existence; for cases $g=3,4$ we determine their…
The New York Times (NYT) games have found widespread popularity in recent years and reportedly account for an increasing fraction of the newspaper's readership. In this paper, we bring the computational lens to the study of New York Times…
We present a different combinatorial interpretations of Lucas and Gibonacci numbers. Using these interpretations we prove several new identities, and simplify the proofs of several known identities. Some open problems are discussed towards…
A brief review of recent research on soliton and black hole solutions of Einstein's equations with nonlinear field sources is presented and some open questions are pointed out.
This is a renovated list of open problems, to appear in: "Affine Algebraic Geometry" conference Proceedings volume in Contemporary Mathematics series of the Amer. Math. Soc. Ed. by Jaime Gutierrez, Vladimir Shpilrain, and Jie-Tai Yu.
Clobber is a new two-player board game. In this paper, we introduce the one-player variant Solitaire Clobber where the goal is to remove as many stones as possible from the board by alternating white and black moves. We show that a…
We introduce a one-person game that we call Padlock Solitaire which resembles the well-known clock solitaire card game. Analyzing variants of this game we obtain simple proofs of some classical results of combinatorics including ballot…
We obtain new BPS solutions of six-dimensional, N = 1 supergravity coupled to a tensor multiplet. These solutions are sourced by multiple "superthreads" carrying D1-D5-P charges and two magnetic dipole charges. These new solutions are…
Contents: 1. Editor's note; 2. gamma-sets from a weak hypothesis; 3. Research announcements; 3.1. Ultrafilters with property (s); 3.2. On a converse to Banach's Fixed Point Theorem; 3.3. Analytic groups and pushing small sets apart 3.4.…
These notes are based on Appalachian Set Theory lectures given by M. Malliaris on November 5, 2016 with D. Casey as the official scribe. The aim of the lectures was to present the setup and some key arguments of "Cofinality spectrum…
I describe work in progress with Baryshnikov and Zharnitsky on periodic billiard orbits that leads one to an exterior differential system (EDS). I then give a brief introduction to EDS illustrated by several examples.
One of the great pleasures of working with Imre Leader is to experience his infectious delight on encountering a compelling combinatorial problem. This collection of open problems in combinatorics has been put together by a subset of his…
We develop a new tool, namely polynomial and linear algebraic methods, for studying systems of word equations. We illustrate its usefulness by giving essentially simpler proofs of several hard problems. At the same time we prove extensions…
We describe a class of combinatorial design problems which typically occur in professional sailing league competitions. We discuss connections to resolvable block designs and equitable coverings and to scheduling problems in operations…
I present the highlights of a long review on polarization in deep inelastic scattering. Some new results are discussed at the end of the talk.
This article presents a new three-player version of the bridge playing card game for the purpose of ending fixed partnerships so that the play can be more dynamic and flexible. By dynamically redefining team makeup in real time, this game…
The billiard systems within quadrics, playing the role of discrete analogues of geodesics on ellipsoids, are incorporated into the theory of integrable quad-graphs. An initial observation is that the Six-pointed star theorem, as the…
CONTENTS: A surprising covering of the real line Unions of chains in dyadic compact spaces and topological groups On the Pytkeev property in spaces of continuous functions Selection principles related to alpha_i-properties On the Kocinac…
These informal notes deal with a number of questions related to sums and integrals in analysis.
In this note we show how techniques developed for untangling planar graphs by Bose et al. [Discrete & Computational Geometry 42(4): 570-585 (2009)] and Goaoc et al. [Discrete & Com- putational Geometry 42(4): 542-569 (2009)] imply new…