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, , and Non-Permutability of -Steps

2012
*
Journal of symbolic computation
*

Using a human-oriented formal example proof

doi:10.1016/j.jsc.2011.12.035
fatcat:g2uh2ml62zgi7bnoffo74dczgi
*of*the (*lim*+) theorem, i.e. that the sum*of*limits is the limit*of*the sum, which is*of*value for reference on its own, we exhibit a*non*-*permutability**of*beta-*steps*...*and*delta+-*steps*(according to Smullyan's classification), which is not visible with*non*-liberalized delta-rules*and*not serious with further liberalized delta-rules, such as the delta++-rule. ... I would also like to thank the lecturers*and*students*of*the course (Autexier et al., 2004/05) ...##
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Permutations avoiding 1324 and patterns in Łukasiewicz paths

2015
*
Journal of the London Mathematical Society
*

In this context, we consider occurrences

doi:10.1112/jlms/jdv020
fatcat:6ekyuwpgozbd3nejx2mozy6o7m
*of*patterns in Łukasiewicz paths*and*prove that in the limit they exhibit a concentrated Gaussian distribution. ... This improves on a previous lower bound*of*9.47. Central to our proof is an examination*of*the asymptotic distributions*of*certain substructures in the Hasse graphs*of*the*permutations*. ... He is also grateful to Robert Brignall*and*an anonymous referee both*of*whom provided useful feedback which helped to improve the presentation. S.D.G. ...##
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Proof terms for infinitary rewriting, progress report
[article]

2014
*
arXiv
*
pre-print

A proof

arXiv:1402.2245v2
fatcat:hp27ys7rvffjpkjydjidyt3lr4
*of*the compression property via proof terms is presented, which establishes*permutation*equivalence between the original*and*the compressed reductions. ... Our main use*of*proof terms is in a definition*of**permutation*equivalence for transfinite reductions, on the basis*of**permutation*equations. ... (*δ*) :=*lim*α→*β*tgt(*δ*[α]). ...##
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Definable maximal cofinitary groups of intermediate size
[article]

2019
*
arXiv
*
pre-print

LetS = S

arXiv:1904.05823v1
fatcat:eudgzxxgdzeypfkrkk7s5hy3je
*δ*:*δ*< ω M be a sequence*of*stationary costationary subsets*of*ω M −1 consisting*of*ordinals*of*cofinality ω M −2*and*such that for*δ*=*δ*′ , S*δ*∩ S*δ*′ is*non*-stationary. ... Furthermore reproducing the ideas*of*[10] , in L[C*δ*] we can find subsets Z*δ*⊆ ω M −1 such that ( * )*δ*: If*β*< ω M −1*and*M is a suitable model such that ω M −2 ⊆ M, (ω M −1 ) M =*β*,*and*Z*δ*∩*β*∈ ...##
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Average output entropy for quantum channels

2011
*
Journal of Mathematical Physics
*

We prove equality

doi:10.1063/1.3658860
fatcat:byjfly6bd5bszgur6aldcb6f7q
*of*the two quantities in some cases, in particular we conclude that for Δ_λ both are*non*-analytic functions*of*the variable λ. ... We find an explicit form for β_r^ for some entanglement-breaking channels,*and*also for the qubit depolarizing channel Δ_λ as a function*of*the parameter λ. ... Lemma 12: Let A be a two-rail channel,*and*[*β*] is the conjugacy class*of*a*permutation*. Then Q restricted to [*β*] is maximal on*non*-overlapping members α ∈ [*β*]. ...##
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Monotonous subsequences and the descent process of invariant random permutations
[article]

2018
*
arXiv
*
pre-print

It is known from the work

arXiv:1805.05253v1
fatcat:x4ccygfej5dnjd5dw6bf7ac4ri
*of*Baik, Deift,*and*Johansson [1999] that we have Tracy-Widom fluctuations for the longest increasing subsequence*of*uniform*permutations*. ... Using similar techniques, we also prove that the limiting descent process*of*a large class*of*random*permutations*is stationary, one-dependent*and*determinantal. ... Acknowledgements The author would like to acknowledge many extremely useful conversations with Adrien Hardy*and*Mylène Maïda, their supervision*of*this work*and*their great help to elaborate*and*to ameliorate ...##
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Concentration inequalities for randomly permuted sums
[article]

2018
*
arXiv
*
pre-print

Initially motivated by the study

arXiv:1805.03579v1
fatcat:i4powfjq2valviltnj7c4fuvay
*of*the*non*-asymptotic properties*of**non*-parametric tests based on*permutation*methods, concentration inequalities for uniformly*permuted*sums have been largely studied ... The idea is to first obtain a rough inequality for the square root*of*the*permuted*sum,*and*then, iterate the previous analysis*and*plug this first inequality to obtain a general concentration*of**permuted*... The first*step*consists in controlling the conditional quantile q 1−α (X n )*and*the second*step*provides an upper-bound for q α 1−*β*/2 . 1st*step*. ...##
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A central limit theorem for the number of descents and some urn models
[article]

2021
*
arXiv
*
pre-print

The purpose

arXiv:1906.02980v3
fatcat:bk7tcu3jhfadvlqhbb2clry3sm
*of*this work is to establish a central limit theorem that can be applied to a particular form*of*Markov chains, including the number*of*descents in a random*permutation**of*𝔖_n, two-type generalized ... Pólya urns,*and*some other urn models. ... So if 3*β*> α*and*S n is the number*of*white balls in the urn after n*steps*, we have S n − α+*β*2 n √ n =⇒ N 0, (α −*β*) 2 (α +*β*) 4(3β − α) . ...##
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Bounds on the diameter of Cayley graphs of the symmetric group
[article]

2012
*
arXiv
*
pre-print

We prove this conjecture for sets

arXiv:1205.1596v1
fatcat:ybsspxooqzgwhj4bmie4qmii34
*of*generators containing a*permutation*fixing at least 37%*of*the points. ... In this paper we are concerned with the conjecture that, for any set*of*generators S*of*the symmetric group*of*degree n, the word length in terms*of*S*of*every*permutation*is bounded above by a polynomial ... Clearly,*lim*n→∞ C(*δ*0 , κ, λ, N, n) = 1. The case*of*"special"*permutations*a is very similar. ...##
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Iteratively Changing the Heights of Automorphism Towers

2012
*
Notre Dame Journal of Formal Logic
*

We extend the results

doi:10.1215/00294527-1715662
fatcat:c4qyj3mp7fembel2nvxtzzhsca
*of*Hamkins*and*Thomas concerning the malleability*of*automorphism tower heights*of*groups by forcing. ... For example, it is possible to increase the height*of*the automorphism tower by passing to a forcing extension, then increase it further by passing to a ground model,*and*then decrease it by passing to ... Since E * γ =*lim**δ*→γ E*δ*, the resulting E * γ coincide,*and*therefore P s γ = P t γ . ...##
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Mathematical structure of magnons in quantum ferromagnets

1999
*
Journal of Physics A: Mathematical and General
*

We provide the mathematical structure

doi:10.1088/0305-4470/32/32/303
fatcat:jqgzoc5k6bbudj2vvsoq2nkptu
*and*a simple, transparent*and*rigorous derivation*of*the magnons as elementary quasi-particle excitations at low temperatures*and*in the infinite spin limit for a ... large class*of*Heisenberg ferromagnets. ... + k))ω(σ 3 )*δ*k,0 | | 1/2 −2*β*h*lim*S→∞ ω(F + S (q)F − S (q))*and**lim*S→∞ ω(F + S (q)F − S (q)) = ω(F + (q)F − (q)). ...##
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The length of the longest common subsequence of two independent mallows permutations

2019
*
The Annals of Applied Probability
*

Since

doi:10.1214/17-aap1351
fatcat:ecghroq6tvffnn3irpvntyphri
*lim*n→∞ n(1 − q n ) =*β**and**lim*n→∞ Thus, for any*δ*> 1, there exists N > 0 such that q n n ∈ e −*β**δ*,*δ*e −*β*, when n > N . ... Therefore, the length*of*the LCS*of*two independent*permutations*is only*of*interest when both*permutations*are*non*-uniformly distributed. 1.1.2 Mallows Measure on Symmetric Group S n Definition 1.1.2. ... Bound LCS via Regenerative Process Constructing Mallows*Permutations*For a given parameter 0 < q < 1, Gnedin*and*Olshanski [14] constructed an infinite Mallows*permutation*with parameter q on N by ...##
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A Generalization of the Erdős–Turán Law for the Order of Random Permutation

2012
*
Combinatorics, probability & computing
*

*and*its generalization for Ewens'

*permutations*associated with sampling from the PD/GEM(θ)-distribution. ... The cycle structure

*of*such a

*permutation*can be associated with the path

*of*a decreasing Markov chain on n integers. ... The work

*of*the second author was partially supported by the Department

*of*Mathematics at Utrecht University

*and*the Dutch stochastics cluster STAR. ...

##
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Bounds on the diameter of Cayley graphs of the symmetric group

2013
*
Journal of Algebraic Combinatorics
*

We prove this conjecture for sets

doi:10.1007/s10801-013-0476-3
fatcat:zrmri62a2fhilkfpowdckl3ooq
*of*generators containing a*permutation*fixing at least 37 %*of*the points. ... In this paper we are concerned with the conjecture that, for any set*of*generators S*of*the symmetric group Sym(n), the word length in terms*of*S*of*every*permutation*is bounded above by a polynomial*of*... The remaining authors would like to express our sorrow at the passing*of*a friend*and*also our deepest thanks to Ákos for his great contribution to mathematics*and*to the lives*of*all*of*us. ...##
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Intervals of permutation class growth rates
[article]

2015
*
arXiv
*
pre-print

We prove that the set

arXiv:1410.3679v2
fatcat:7i5poymeqvg35dyjv3pcbj7rym
*of*growth rates*of**permutation*classes includes an infinite sequence*of*intervals whose infimum is θ_B≈2.35526,*and*that it also contains every value at least λ_B≈2.35698. ... Our proof is based upon an analysis*of*expansions*of*real numbers in*non*-integer bases, the study*of*which was initiated by Rényi in the 1950s. ... He would also like to thank Vince, Robert Brignall*and*two referees for reading earlier drafts*of*this paper; their feedback resulted in significant improvements to its presentation. S.D.G. ...
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