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Supersolvable LL-lattices of binary trees

2005
*
Discrete Mathematics
*

Some posets

doi:10.1016/j.disc.2005.03.005
fatcat:tpcwygoibrg5nbpzy5rezv4jba
*of**binary*leaf-labeled*trees*are shown to be*supersolvable**lattices*and explicit EL-labelings are given. ... A finite graded*lattice**of*rank n is*supersolvable*if and only if it is S n EL-shellable. Poset*of*forests A*tree*is a leaf-labeled rooted*binary**tree*and a forest is a set*of*such*trees*. ... Introduction The aim*of*this article is to study some posets on forests*of**binary*leaf-labeled*trees*. ...##
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Supersolvable LL-lattices of binary trees
[article]

2003
*
arXiv
*
pre-print

Some posets

arXiv:math/0304132v1
fatcat:oqrl7jdr6fbv5gs42bmbspbdka
*of**binary*leaf-labeled*trees*are shown to be*supersolvable**lattices*and explicit EL-labelings are given. ... Poset*of*forests A*tree*is a leaf-labeled rooted*binary**tree*and a forest is a set*of*such*trees*. Vertices are either inner vertices (valence 3) or leaves and roots (valence 1). ... The Möbius function*of*P , µ : Int(P ) → Z, is defined recursively by*supersolvable**lattices*include modular*lattices*, the partition*lattice*Π n and the*lattice**of*subgroups*of*a finite*supersolvable*group ...##
###
Author index to volume 296

2005
*
Discrete Mathematics
*

Chapoton,

doi:10.1016/s0012-365x(05)00315-8
fatcat:m2gwquhb4zcw5h3uc4nmsxjc2u
*Supersolvable**LL*-*lattices**of**binary**trees*(1) 1-13 Bonoli, G. and O. Polverino, The twisted cubic in PGð3; qÞ and translation spreads in HðqÞ , T. and C.G. ... Zhang, Sharp upper and lower bounds for largest eigenvalue*of*the Laplacian matrices*of**trees*(2-3) 187-197 Hung, L.X., see N.D. Tan (1) 59-72 Hurlbert, G.H., see B. ...##
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Factorization of the Characteristic Polynomial

2014
*
Discrete Mathematics & Theoretical Computer Science
*

We will see that Stanley's

doi:10.46298/dmtcs.2386
fatcat:6ywjqlek6jawvizpm4w5kphspa
*Supersolvability*Theorem is a corollary*of*this result. ... International audience We introduce a new method for showing that the roots*of*the characteristic polynomial*of*a finite*lattice*are all nonnegative integers. ... Additionally, he showed these roots where counted by the sizes*of*blocks in a partition*of*the atom set*of*the*lattice*. Blass and Sagan [BS97] extended this result to*LL**lattices*. ...##
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Whitney numbers of some geometric lattices

1994
*
Journal of combinatorial theory. Series A
*

It is worth noting that, from the work

doi:10.1016/0097-3165(94)90034-5
fatcat:aoqcqqs2cnfs7p2g7z3tfts3wm
*of*Aigner [Aig2] , this problem has an affirmative answer when restricted to the case*of**binary**lattices*. ... ,L ..... be a chain*of**supersolvable*geometric*lattices**of*rank O, 1, 2, ..., n .... in ql. ...##
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Factoring the characteristic polynomial of a lattice

2015
*
Journal of combinatorial theory. Series A
*

We introduce a new method for showing that the roots

doi:10.1016/j.jcta.2015.06.006
fatcat:3776hbua5jbvhkskfsccqhoa4m
*of*the characteristic polynomial*of*certain finite*lattices*are all nonnegative integers. ... We will see that Stanley's*Supersolvability*Theorem is a corollary*of*this result. Additionally, we will prove a theorem which gives three conditions equivalent to factorization. ... Acknowledgments The authors would like to thank Torsten Hoge for pointing out the connection*of*Theorem 11 with Terao's theorem about nice partitions in central hyperplane arrangements. ...##
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A LL-lattice reformulation of arithmetree over planar rooted trees. Part II
[article]

2004
*
arXiv
*
pre-print

We propose a 'deformation'

arXiv:math/0408349v1
fatcat:e2xqeoq3zbe6fkupxwvo6sxbru
*of*a vectorial coding used in Part I, giving a*LL*-*lattice*on rooted planar*trees*according to the terminology*of*A. Blass and B. E. Sagan. ... Our parenthesis framework allows a more tractable reformulation to explore the properties*of*the underlying*lattice*describing operations and simplify a proof*of*a fundamental theorem related to arithmetics ... Blass [8, 1] , we compute the Möbius function*of*these*lattices*and proved they are*of*type*LL*(like for the Tamari*lattices*Y n orN n associated with planar*binary**trees*). ...##
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Factoring the characteristic polynomial of a lattice
[article]

2015
*
arXiv
*
pre-print

We introduce a new method for showing that the roots

arXiv:1403.0666v2
fatcat:hpbjhhtzmfdp7lkabwzk6cffly
*of*the characteristic polynomial*of*certain finite*lattices*are all nonnegative integers. ... We will see that Stanley's*Supersolvability*Theorem is a corollary*of*this result. Additionally, we will prove a theorem which gives three conditions equivalent to factorization. ... Acknowledgments The authors would like to thank Torsten Hoge for pointing out the connection*of*Theorem 11 with Terao's theorem about nice partitions in central hyperplane arrangements. ...##
###
Applications of Quotient Posets
[article]

2014
*
arXiv
*
pre-print

Blass and Sagan's result about

arXiv:1411.3022v1
fatcat:rkcla744m5atzg7tsv552bjgpy
*LL**lattices*will also be shown to be a consequence*of*our factorization theorems. ... Our factorization theorems will then be used to show that any interval*of*the Tamari*lattice*has a characteristic polynomial which factors in this way. ... We will use this fact to prove Blass and Sagan's result about*LL**lattices*[2] which is a generalization*of*the*supersolvability*result. ...##
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Factorization of the Characteristic Polynomial of a Lattice using Quotient Posets

2014
unpublished

We will see that Stanley's

fatcat:iiwyyk6fczdqbcfzxjzercnapq
*Supersolvability*Theorem is a corollary*of*this result. ... We introduce a new method for showing that the roots*of*the characteristic polynomial*of*a finite*lattice*are all nonnegative integers. ... Additionally, he showed these roots where counted by the sizes*of*blocks in a partition*of*the atom set*of*the*lattice*. Blass and Sagan [BS97] extended this result to*LL**lattices*. ...