Do you want to publish a course? Click here

Partition properties of the dense local order and a colored version of Millikens theorem

156   0   0.0 ( 0 )
 Publication date 2008
  fields
and research's language is English




Ask ChatGPT about the research

We study the finite dimensional partition properties of the countable homogeneous dense local order. Some of our results use ideas borrowed from the partition calculus of the rationals and are obtained thanks to a strengthening of Millikens theorem on trees.



rate research

Read More

131 - Andreas Holmsen 2013
We give the following extension of Baranys colorful Caratheodory theorem: Let M be an oriented matroid and N a matroid with rank function r, both defined on the same ground set V and satisfying rank(M) < rank(N). If every subset A of V with r(V - A) < rank (M) contains a positive circuit of M, then some independent set of N contains a positive circuit of M.
We prove a quantitative version of the multi-colored Motzkin-Rabin theorem in the spirit of [BDWY12]: Let $V_1,ldots,V_n subset R^d$ be $n$ disjoint sets of points (of $n$ `colors). Suppose that for every $V_i$ and every point $v in V_i$ there are at least $delta |V_i|$ other points $u in V_i$ so that the line connecting $v$ and $u$ contains a third point of another color. Then the union of the points in all $n$ sets is contained in a subspace of dimension bounded by a function of $n$ and $delta$ alone.
168 - Felix Joos , Jaehoon Kim 2019
For a collection $mathbf{G}={G_1,dots, G_s}$ of not necessarily distinct graphs on the same vertex set $V$, a graph $H$ with vertices in $V$ is a $mathbf{G}$-transversal if there exists a bijection $phi:E(H)rightarrow [s]$ such that $ein E(G_{phi(e)})$ for all $ein E(H)$. We prove that for $|V|=sgeq 3$ and $delta(G_i)geq s/2$ for each $iin [s]$, there exists a $mathbf{G}$-transversal that is a Hamilton cycle. This confirms a conjecture of Aharoni. We also prove an analogous result for perfect matchings.
77 - D. Borthwick , S. Graffi 2004
Consider in $L^2 (R^l)$ the operator family $H(epsilon):=P_0(hbar,omega)+epsilon Q_0$. $P_0$ is the quantum harmonic oscillator with diophantine frequency vector $om$, $Q_0$ a bounded pseudodifferential operator with symbol holomorphic and decreasing to zero at infinity, and $epinR$. Then there exists $ep^ast >0$ with the property that if $|ep|<ep^ast$ there is a diophantine frequency $om(ep)$ such that all eigenvalues $E_n(hbar,ep)$ of $H(ep)$ near 0 are given by the quantization formula $E_alpha(hbar,ep)= {cal E}(hbar,ep)+laom(ep),alpharahbar +|om(ep)|hbar/2 + ep O(alphahbar)^2$, where $alpha$ is an $l$-multi-index.
We obtain a unification of two refinements of Eulers partition theorem respectively due to Bessenrodt and Glaisher. A specialization of Bessenrodts insertion algorithm for a generalization of the Andrews-Olsson partition identity is used in our combinatorial construction.
comments
Fetching comments Fetching comments
Sign in to be able to follow your search criteria
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا