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### Counting forests

Lajos Takács
1990 Discrete Mathematics
Cayley stated that the number of forests with n labeled vertices that consist of s distinct trees such that s specified vertices belong to distinct trees is snn-'-' for 1 <s c n.  ...  Introduction A forest is a simple graph that has no cycles. In other words, a forest is simple graph, all of whose components are trees.  ...  Denote by F(n, s), 1 GS G 12, the number of forests having vertex set {I, 2,, * . * 9 n} and s components which are trees such that vertices 1,2, . . . , s all belong to different trees.  ...

### Counting bi-colored A'Campo forests [article]

Noémie Combe, Vincent Jugé
2017 arXiv   pre-print
We deduce an algorithm to count these forests in polynomial time, answering an open question of A'Campo.  ...  We give an efficient method of counting bi-colored A'Campo forests and provide a stratification criterion for the space of those graphs.  ...  Counting A'Campo forests Canonical splittings of configurations pave the way to recursive decompositions of configurations, leading to the enumeration of our graphs.  ...

### Counting rooted forests in a network [article]

Oliver Knill
2013 arXiv   pre-print
If a forest with an even number of edges is called even, then det(1-L) is the difference between even and odd rooted spanning forests in G.  ...  We use a recently found generalization of the Cauchy-Binet theorem to give a new proof of the Chebotarev-Shamis forest theorem telling that det(1+L) is the number of rooted spanning forests in a finite  ...  We can also look at k = −1, in which case we count forests with odd number of trees with a negative sign.  ...

### Forest languages defined by counting maximal paths [article]

Martin Beaudry
2021 arXiv   pre-print
A leaf path language is a Boolean combination of sets of the form ^𝗆𝖤^k L, with k ≥ 1 and L a regular word language, which consist of those forests where the node labels in at least k leaf-to-root paths  ...  We prove the existence of an algorithm that, given a regular forest language, returns in finite time a sequence of such algebras; their wreath product is divided by the language's syntactic algebra if,  ...  count sticks.  ...

### On Cayley's formula for counting forests

Lajos Takács
1990 Journal of combinatorial theory. Series A
INTRODUCTION A forest is a simple graph that has no cycles. In other words, a forest is a simple graph, all of whose components are trees.  ...  The number of such forests is F(n -1, s +j -1). If we add ('7 ") F(n -1, s + j -1) for all possible values of j we obtain F(n, s). This proves (3).  ...

### Counting Forests by Descents and Leaves

Ira M. Gessel
1995 Electronic Journal of Combinatorics
We show that the number of forests of rooted trees on a given vertex set with \$i+1\$ leaves and \$j\$ descents is equal to the number with \$j+1\$ leaves and \$i\$ descents.  ...  Rather than counting forests directly, we first count some related objects.  ...  It follows from (2) that βU(x; α, β) = C x(1 − α); β 1 − α , α 1 − α . (3) Next, we describe a decomposition for marked forests that allows us to count them.  ...

### Lyman-Alpha Forest Correlations Using Neighbor Counts

Avery Meiksin, Franois R. Bouchet
1995 Astrophysical Journal
The technique appears to reduce the scatter in estimates of the correlation function by a factor of about two from the traditional pair-counting method.  ...  We apply the technique to the Lyman-alpha forest line lists determined from the spectra of seven z > 2 QSOs observed at high resolution ( < 25 km/s ).  ...  DISCUSSION The strongest evidence for a deviation from Poisson statistics in the Ly␣ forests analyzed is provided by the cumulative distributions of cell counts.  ...

### Parameterized counting of trees, forests and matroid bases [article]

Cornelius Brand, Marc Roth
2016 arXiv   pre-print
We investigate the complexity of counting trees, forests and bases of matroids from a parameterized point of view.  ...  (ICALP 2015), the hardness result for k-forests implies # W-hardness of the problem of counting bases of a matroid when parameterized by rank or nullity, even if the matroid is restricted to be representable  ...  The parameterized complexity of counting trees and forests In this section we will prove that counting k-trees and k-forests is #W-hard.  ...

### Lyman Alpha Forest Clustering Using Cell Counts Statistics [article]

François R. Bouchet, Avery Meiksin
1995 arXiv   pre-print
We present a novel technique for calculating forest correlations based on cell counts. It is applied to the line lists from 7 QSOs observed at high resolution (Δ v<25).  ...  If this first detection of anti-correlations is physical, additional factors to gravity may play a role in determining the clustering of the forest on comoving scales > 3h^-1.  ...  The pair count estimate of Cristiani et al. yielded no evidence for clustering in this range.  ...

### Estimating Forest Recreation Demand Using Count Data Models [chapter]

Jeffrey E. Englin, Thomas P. Holmes, Erin O. Sills
2003 Forestry sciences
In section 3, we use count data models to estimate the value of rain forest protection in Brazil.  ...  APPLICATION: RAIN FOREST VALUATION To demonstrate how count data methods can be applied to real world forestry problems, we present a case study of tropical rain forest protection in southern Brazil.  ...

### Considerations towards a Novel Approach for Integrating Angle-Count Sampling Data in Remote Sensing Based Forest Inventories

2017 Forests
Integration of remote sensing (RS) data in forest inventories for enhancing plot-based forest variable prediction is a widely researched topic.  ...  Achieving geometric consistency is particularly difficult with regard to angle-count sampling (ACS) plots, which have neither distinct shape nor distinct extent.  ...  Forests 2017, 8 Figure 3 . 83 Example of selected pixels (blue crosses) in three different plots for each transfer angle-count sampling (tACS) data set.  ...

### A note on Prüfer-like coding and counting forests of uniform hypertrees [article]

Christian Lavault
2011 arXiv   pre-print
It is a simple extension of the classical Prüfer code for (labelled) rooted trees to an encoding for forests of (labelled) rooted uniform hypertrees and hypercycles, which allows to count them up according  ...  This note presents an encoding and a decoding algorithms for a forest of (labelled) rooted uniform hypertrees and hypercycles in linear time, by using as few as n - 2 integers in the range [1,n].  ...  In the above Eq. (2) indeed, the left-hand factor (between brackets) counts the number of forests of rooted b-uniform hypertrees, while the right-hand one counts the number of smooth hypercycles labelled  ...

### Counting Rooted Spanning Forests For Circulant Foliation Over A Graph [article]

Liliya Grunwald, Young Soo Kwon, Ilya Mednykh
2021 arXiv   pre-print
In this paper, we present a new method to produce explicit formulas for the number of rooted spanning forests f(n) for the infinite family of graphs H_n=H_n(G_1, G_2,...  ...  We prove that the number of rooted spanning forests can be represented in the form f(n)=p f(H)a(n)^2, where a(n) is an integer sequence and p is a prescribed natural number depending on the number of odd  ...  The aim of the present paper is to investigate analytical, arithmetical and asymptotic properties of function counting the number of rooted spanning forests in circulant foliation over a given graph.  ...

### Bayesian Spatial Analysis of Hardwood Tree Counts in Forests via MCMC [article]

Reihaneh Entezari, Patrick E. Brown, Jeffrey S. Rosenthal
2018 arXiv   pre-print
In this paper, we perform Bayesian Inference to analyze spatial tree count data from the Timiskaming and Abitibi River forests in Ontario, Canada.  ...  How spatial predictions for new sites in the forests change as the amount of training data is reduced is studied and compared with a Logistic Regression model without a spatial effect.  ...  1 Introduction The forest inventory problem The forest industry has a significant impact on the economy of countries such as Canada, making forests an important financial asset.  ...

### The effects of truncating the angle count sampling method on the Austrian National Forest Inventory

Ambros Berger, Thomas Gschwantner, Klemens Schadauer
2020 Annals of Forest Science
. & Context The Austrian National Forest Inventory changed its plot design to angle count sampling plots that are limited to circles of 300 m 2 .  ...  & Key message Truncating the angle count sampling plots leads to a higher stock estimate because fewer trees are missed.  ...  Because we are counting trees of this size and above, the remaining trees have to be fewer than 25%.  ...
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