27,186 research outputs found
A proof of Mader's conjecture on large clique subdivisions in -free graphs
Given any integers , we show there exists some such
that any -free graph with average degree contains a subdivision of
a clique with at least vertices. In particular,
when this resolves in a strong sense the conjecture of Mader in 1999 that
every -free graph has a subdivision of a clique with order linear in the
average degree of the original graph. In general, the widely conjectured
asymptotic behaviour of the extremal density of -free graphs suggests
our result is tight up to the constant .Comment: 25 pages, 1 figur
Discussion of: A statistical analysis of multiple temperature proxies: Are reconstructions of surface temperatures over the last 1000 years reliable?
Discussion of "A statistical analysis of multiple temperature proxies: Are
reconstructions of surface temperatures over the last 1000 years reliable?" by
B.B. McShane and A.J. Wyner [arXiv:1104.4002]Comment: Published in at http://dx.doi.org/10.1214/10-AOAS398C the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A Distributive Lattice Connected with Arithmetic Progressions of Length Three
Let be a collection of 3-element subsets of with the property that if and are two 3-element
subsets in , then there exists an integer sequence such that and are arithmetic progressions.
We determine the number of such collections and the number of
them of maximum size. These results confirm two conjectures of Noam Elkies.Comment: 25 pages, 1 figure. To appear in the Ramanujan Journa
The Lecture Hall Parallelepiped
The s-lecture hall polytopes P_s are a class of integer polytopes defined by
Savage and Schuster which are closely related to the lecture hall partitions of
Eriksson and Bousquet-M\'elou. We define a half-open parallelopiped Par_s
associated with P_s and give a simple description of its integer points. We use
this description to recover earlier results of Savage et al. on the
\delta-vector (or h^*-vector) and to obtain the connections to s-ascents and
s-descents, as well as some generalizations of these results.Comment: 14 pages. To appear in Annals of Combinatoric
The Heisenberg Relation - Mathematical Formulations
We study some of the possibilities for formulating the Heisenberg relation of
quantum mechanics in mathematical terms. In particular, we examine the
framework discussed by Murray and von Neumann, the family (algebra) of
operators affiliated with a finite factor (of infinite linear dimension)
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