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Counting forests

1990
*
Discrete Mathematics
*

Cayley stated that the number of

doi:10.1016/0012-365x(90)90139-9
fatcat:qa5vwusmvbgr3l2jjyyuhissp4
*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. ...##
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Counting bi-colored A'Campo forests
[article]

2017
*
arXiv
*
pre-print

We deduce an algorithm to

arXiv:1702.07672v1
fatcat:7b4wjlmspzahzn4toemzwvd7ki
*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. ...##
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Counting rooted forests in a network
[article]

2013
*
arXiv
*
pre-print

If a

arXiv:1307.3810v2
fatcat:uj34kmkstbhrxofnrcs2beydmu
*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. ...##
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Forest languages defined by counting maximal paths
[article]

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

arXiv:2105.09970v2
fatcat:dxyxr6mwyzguzoptajhybcr4sq
*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. ...##
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On Cayley's formula for counting forests

1990
*
Journal of combinatorial theory. Series A
*

INTRODUCTION A

doi:10.1016/0097-3165(90)90064-4
fatcat:s55pjck4m5bgrj7qyndcw5lp3i
*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). ...##
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Counting Forests by Descents and Leaves

1995
*
Electronic Journal of Combinatorics
*

We show that the number of

doi:10.37236/1266
fatcat:z3yx55iw55d3xnnhg3qg3ndi5q
*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. ...##
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Lyman-Alpha Forest Correlations Using Neighbor Counts

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-

doi:10.1086/309608
fatcat:fszbxo75zjhv7pyqgclrt3cnya
*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*. ...##
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Parameterized counting of trees, forests and matroid bases
[article]

2016
*
arXiv
*
pre-print

We investigate the complexity of

arXiv:1611.01823v1
fatcat:mzq5iqfqsrgufczdc2seww63km
*counting*trees,*forests*and bases of matroids from a parameterized point of view. ... (ICALP 2015), the hardness result for k-*forests*implies # W[1]-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[1]-hard. ...##
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Lyman Alpha Forest Clustering Using Cell Counts Statistics
[article]

1995
*
arXiv
*
pre-print

We present a novel technique for calculating

arXiv:astro-ph/9507033v1
fatcat:4tuqcbdxqff5xghnxwxi4hid7a
*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. ...##
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Estimating Forest Recreation Demand Using Count Data Models
[chapter]

2003
*
Forestry sciences
*

In section 3, we use

doi:10.1007/978-94-017-0219-5_19
fatcat:6kfy3o4e7jaadolas3z6nhg5oa
*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. ...##
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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

doi:10.3390/f8070239
fatcat:l5pzkcy5tfathfpjxbbtwog6ii
*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. ...##
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A note on Prüfer-like coding and counting forests of uniform hypertrees
[article]

2011
*
arXiv
*
pre-print

It is a simple extension of the classical Prüfer code for (labelled) rooted trees to an encoding for

arXiv:1110.0204v1
fatcat:vj3w4qdnubffzpluzewojg5bxm
*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 ...##
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Counting Rooted Spanning Forests For Circulant Foliation Over A Graph
[article]

2021
*
arXiv
*
pre-print

In this paper, we present a new method to produce explicit formulas for the number of rooted spanning

arXiv:2111.04297v1
fatcat:wok6iwewczdbbhqbczb6uoahsi
*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. ...##
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Bayesian Spatial Analysis of Hardwood Tree Counts in Forests via MCMC
[article]

2018
*
arXiv
*
pre-print

In this paper, we perform Bayesian Inference to analyze spatial tree

arXiv:1807.01239v1
fatcat:jclyvgd4nne3vg664hw5xgk2kq
*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. ...##
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The effects of truncating the angle count sampling method on the Austrian National Forest Inventory

2020
*
Annals of Forest Science
*

. & Context The Austrian National

doi:10.1007/s13595-019-0907-y
fatcat:3qumacimgff3bbsitvw7ojlmui
*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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