相关论文: Shannon capacity, Chess, DNA and Umbrellas

This paper provides new observations on the Lov\'{a}sz $\theta$-function of graphs. These include a simple closed-form expression of that function for all strongly regular graphs, together with upper and lower bounds on that function for…

In imperfect information games, the evaluation of a game state not only depends on the observable world but also relies on hidden parts of the environment. As accessing the obstructed information trivialises state evaluations, one approach…

A set of graphs is said to be independent if there is no homomorphism between distinct graphs from the set. We consider the existence problems related to the independent sets of countable graphs. While the maximal size of an independent set…

Shannon's channel coding theorem characterizes the maximal rate of information that can be reliably transmitted over a communication channel when optimal encoding and decoding strategies are used. In many scenarios, however, practical…

We obtain some new upper bounds on the maximum number $f(n)$ of edges in $n$-vertex graphs without containing cycles of length four. This leads to an asymptotically optimal bound on $f(n)$ for a broad range of integers $n$ as well as a…

The consideration of the N-body gravitational problem equations can give to us some class of boundary-value problems defined on the "beem's" construction. One can considere it as weak or so-called finite element method's approximation with…

We use the formalism of 'Maximum Principle of Shannon's Entropy' to derive the general power law distribution function, using what seems to be a reasonable physical assumption, namely, the demand of a constant mean "internal order"…

We give the first nonconstant lower bounds for the approximability of the Independent Set Problem on the Power Law Graphs. These bounds are of the form $n^{\epsilon}$ in the case when the power law exponent satisfies $\beta <1$. In the case…

We discuss how to find the well-covered dimension of a graph that is the Cartesian product of paths, cycles, complete graphs, and other simple graphs. Also, a bound for the well-covered dimension of $K_n\times G$ is found, provided that $G$…

In this paper we research a model of multilayer circuits with a single logical layer. We consider $\lambda$-separable graphs as a support for circuits. We establish the Shannon function lower bound $\max \bigl(\frac{2^n}{n}, \frac{2^n (1 -…

A solution to a problem of Erd\H{o}s, Rubin and Taylor is obtained by showing that if a graph $G$ is $(a:b)$-choosable, and $c/d > a/b$, then $G$ is not necessarily $(c:d)$-choosable. The simplest case of another problem, stated by the same…

Shannon's analysis of the fundamental capacity limits for memoryless communication channels has been refined over time. In this paper, the maximum volume $M_\avg^*(n,\epsilon)$ of length-$n$ codes subject to an average decoding error…

In order to study the fundamental limits of network densification, we look at the spatial spectral efficiency gain achieved when densely deployed communication devices embedded in the $d$-dimensional Euclidean space are optimally `matched'…

The scramble number of a graph, a natural generalization of bramble number, is an invariant recently developed to study chip-firing games and graph gonality. We introduce the carton number of a graph, defined to be the minimum size of a…

We prove an explicit upper bound on the amount of entanglement required by any strategy in a two-player cooperative game with classical questions and quantum answers. Specifically, we show that every strategy for a game with n-bit questions…

Witsenhausen's problem asks for the maximum fraction $\alpha_n$ of the $n$-dimensional unit sphere that can be covered by a measurable set containing no pairs of orthogonal points. The best upper bounds for $\alpha_n$ are given by…

Channel symmetry properties that imply the tightness of Shannon's random coding inner bound have recently been used to determine the capacity region of discrete-memoryless two-way channels (DM-TWCs). For channels without such symmetry…

The $k$-th $p$-power of a graph $G$ is the graph on the vertex set $V(G)^k$, where two $k$-tuples are adjacent iff the number of their coordinates which are adjacent in $G$ is not congruent to 0 modulo $p$. The clique number of powers of…

The core of this note is the observation that links between circle packings of graphs and potential theory developed in \cite{BeSc01} and \cite{HS} can be extended to higher dimensions. In particular, it is shown that every limit of finite…

Using the Lieb-Robinson inequality and the continuity property of the quantum capacities in terms of the diamond norm, we derive an upper bound on the values that these capacities can attain in spin-network communication i.i.d. models of…