Graph-counting polynomials for oriented graphs
Reads0
Chats0
TLDR
In this article, the authors consider oriented graphs and discuss some cases where a set of unbranched subgraphs of a finite graph can be represented by a graph-counting polynomial.Abstract:
If ${\cal F}$ is a set of subgraphs $F$ of a finite graph $E$ we define a graph-counting polynomial $$ p_{\cal F}(z)=\sum_{F\in{\cal F}}z^{|F|} $$ In the present note we consider oriented graphs and discuss some cases where ${\cal F}$ consists of unbranched subgraphs $E$. We find several situations where something can be said about the location of the zeros of $p_{\cal F}$.read more
Citations
More filters
A Complete Bibliography of the Journal of Statistical Physics: 2000{2009
TL;DR: In this paper, Zuc11b et al. this paper showed that 1 ≤ p ≤ ∞ [Dud13]. 1/f [HPF15], 1/n [Per17] and 1/m [DFL17] were the most frequent p ≤ p ≥ ∞.
References
More filters
Journal ArticleDOI
Central limit theorems, Lee-Yang zeros, and graph-counting polynomials
TL;DR: The asymptotic normalcy of families of random variables $X$ which count the number of occupied sites in some large set is considered, and sufficient criteria is given, involving the location of the zeros of $P(z)$, for these families to satisfy a central limit theorem (CLT) and even a local CLT (LCLT).
Journal ArticleDOI
Characterization of Lee-Yang polynomials
TL;DR: The Lee-Yang circle theorem describes complex polynomials of degree n in z with all their zeros on the unit circle jzj D 1 as mentioned in this paper, which are obtained by taking z1 D D zn D z in certain multiaffine polynomorphs.
Journal ArticleDOI
Zeros of Graph-Counting Polynomials
TL;DR: In this paper, the authors define a family of subgraphs by restricting the number of edges of a subgraph with endpoint at any vertex of a given graph. And they give precise information on the location of zeros of the subgraph (zeros all real negative, all imaginary).
Journal ArticleDOI
Counting Unbranched Subgraphs
TL;DR: In this article, the polynomial Q(z) e ΣF ∈ Uz cardF associates a weight zcardF to each unbranched subgraph F of length cardF.
Journal ArticleDOI
Location of the Lee-Yang zeros and absence of phase transitions in some Ising spin systems
TL;DR: In this paper, the authors consider a class of Ising spin systems on a set of sites, where sites are grouped into units with the property that each site belongs to either one or two units and the total internal energy of the system is the sum of the energies of the individual units, which in turn depend only on the number of up spins in the unit.