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Berczi K.,MTA ELTE Egervary Research Group | Bernath A.,MTA ELTE Egervary Research Group | Vizer M.,MTA Alfred Renyi Institute of Mathematics
Electronic Journal of Combinatorics | Year: 2015

An undirected simple graph G = (V,E) is called antimagic if there exists an injective function f: E → {1,…|E|} such that (formula presented) for any pair of different nodes u, v ∈ V. In this note we prove - with a slight modification of an argument of Cranston et al. - that k-regular graphs are antimagic for k ≥ 2. © 2015, Australian National University. All rights reserved.

Carassus L.,University of Reims Champagne Ardenne | Rasonyi M.,MTA Alfred Renyi Institute of Mathematics
Mathematics of Operations Research | Year: 2016

This paper investigates the problem of maximizing expected terminal utility in a (generically incomplete) discrete-time financial market model with finite time horizon. By contrast to the standard setting, a possibly nonconcave utility function U is considered, with domain of definition equal to the whole real line. Simple conditions are presented that guarantee the existence of an optimal strategy for the problem. In particular, the asymptotic elasticity of U plays a decisive role: Existence can be shown when it is strictly greater at -∞ than at C +∞. © 2016 INFORMS.

Katona G.O.H.,MTA Alfred Renyi Institute of Mathematics | Nagy D.T.,Eotvos Lorand University
Order | Year: 2015

Let (Formula presented.) be the poset generated by the subsets of [n] with the inclusion relation and let (Formula presented.) be a finite poset. We want to embed (Formula presented.) as many times as possible such that the subsets in different copies are incomparable. The maximum number of such embeddings is asymptotically determined for all finite posets(Formula presented.), where (Formula presented.) denotes the minimal size of the convex hull of a copy of (Formula presented.). We discuss both weak and strong (induced) embeddings. © 2014, Springer Science+Business Media Dordrecht.

Blomer V.,Mathematisches Institute | Maga P.,MTA Alfred Renyi Institute of Mathematics
Selecta Mathematica, New Series | Year: 2016

Let F be an L2-normalized Hecke Maaß cusp form for Γ 0(N) ⊆ SL n(Z) with Laplace eigenvalue λF. If Ω is a compact subset of Γ 0(N) \ PGL n/ PO n, we show the bound ‖F|Ω‖∞≪ΩNελFn(n-1)/8-δ for some constant δ= δn> 0 depending only on n. © 2016, Springer International Publishing.

Backhausz A.,MTA Alfred Renyi Institute of Mathematics | Backhausz A.,Eotvos Lorand University | Szegedy B.,MTA Alfred Renyi Institute of Mathematics | Virag B.,MTA Alfred Renyi Institute of Mathematics | Virag B.,University of Toronto
Random Structures and Algorithms | Year: 2015

Let G be a d-regular graph of sufficiently large-girth (depending on parameters k and r) and μ be a random process on the vertices of G produced by a randomized local algorithm of radius r. We prove the upper bound (k+1-2k/d)(1d-1)k for the (absolute value of the) correlation of values on pairs of vertices of distance k and show that this bound is optimal. The same results hold automatically for factor of i.i.d processes on the d-regular tree. In that case we give an explicit description for the (closure) of all possible correlation sequences. Our proof is based on the fact that the Bernoulli graphing of the infinite d-regular tree has spectral radius 2d-1. Graphings with this spectral gap are infinite analogues of finite Ramanujan graphs and they are interesting on their own right. © 2015 Wiley Periodicals, Inc.

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