Related papers: Tricky Arithmetic
We describe a new variation of a mathematical card trick, whose analysis leads to new lower bounds for data compression and estimating the entropy of Markov sources.
These are lecture notes for lectures at the Park City Math Institute, summer 2007. We cover aspects of the dimer model on planar, periodic bipartite graphs, including local statistics, limit shapes and fluctuations.
These are lecture notes from my talks at the "Current Developments in Mathematics" conference (Harvard, 2006). They cover a variety of topics involving symplectic cohomology. In particular, a discussion of (algorithmic) classification…
An informal and elementary introduction to probability scoring and forecast verification and improvement, slightly extended from Significance 22:3(2025)16, which might be useful for less mathematical readers as a prologue to the classic…
This paper is around the topics I discussed in the lecture I gave at the Isaac Newton Institute in Cambridge, July 2009, in the Introductory Workshop. This paper can be read as a companion to my paper [Sa\"i di], where detailed proofs can…
We detail the rules and mathematical structure of Al-Jabar, a game invented by the authors based on intuitive concepts of color-mixing and ideas from abstract algebra. Game-play consists of manipulating colored game pieces; we discuss how…
Zaremba's Conjecture concerns the formation of continued fractions with partial quotients restricted to a given alphabet. In order to answer the numerous questions that arrive from this conjecture, it is best to consider a semi-group, often…
This is a paper in Analytic Topology.
A Comment on the Letter by Raphael Blumenfeld and Sam F. Edwards, [Phys. Rev. Lett. 90, 114303 (2003)].
Consider a collection of weighted subsets of a ground set N. Given a query subset Q of N, how fast can one (1) find the weighted sum over all subsets of Q, and (2) sample a subset of Q proportionally to the weights? We present a tree-based…
Rejoinder: Fisher Lecture: Dimension Reduction in Regression [arXiv:0708.3774]
This paper is a criticism on "A Mathematician's Apology" by G. H. Hardy.
This review is the updated and enlarged version of a talk delivered by J. S. on the occasion of the 1982 meeting of Nobel laureates at Lindau, and of talks given by B.-G. E. at several West German universities and Max Planck institutes in…
New cases of the multiplicity conjecture are considered.
This is a pedagogical article cited in the foregoing research note, quant-ph/9911050
The results in the preceding comment are placed on a more general mathematical foundation.
The results of several papers concerning the \v{C}ern\'y conjecture are deduced as consequences of a simple idea that I call the averaging trick. This idea is implicitly used in the literature, but no attempt was made to formalize the proof…
The concept of approximation gain was introduced recently by M\"uller and Taktikos for some abc-triples related to convergents of surds, where there is a relatively large gap between min{a,b,c} and max{a,b,c}. This note proposes a…
These are lecture notes that arose from a representation theory course given by the first author to the remaining six authors in March 2004 within the framework of the Clay Mathematics Institute Research Academy for high school students,…
At a conference in Debrecen in October 2010 Nathanson announced some results concerning the arithmetic diameters of certain sets. He proposed some related results on the representation of integers by sums or differences of powers of 2 and…