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, , and Non-Permutability of -Steps

Claus-Peter Wirth
2012 Journal of symbolic computation  
Using a human-oriented formal example proof 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)  ... 
doi:10.1016/j.jsc.2011.12.035 fatcat:g2uh2ml62zgi7bnoffo74dczgi

Permutations avoiding 1324 and patterns in Łukasiewicz paths

David Bevan
2015 Journal of the London Mathematical Society  
In this context, we consider occurrences 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.  ... 
doi:10.1112/jlms/jdv020 fatcat:6ekyuwpgozbd3nejx2mozy6o7m

Proof terms for infinitary rewriting, progress report [article]

Carlos Lombardi, Alejandro Ríos, Roel de Vrijer
2014 arXiv   pre-print
A proof 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]).  ... 
arXiv:1402.2245v2 fatcat:hp27ys7rvffjpkjydjidyt3lr4

Definable maximal cofinitary groups of intermediate size [article]

Vera Fischer, Sy David Friedman, David Schrittesser, Asger Törnquist
2019 arXiv   pre-print
LetS = S 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 δβ ∈  ... 
arXiv:1904.05823v1 fatcat:eudgzxxgdzeypfkrkk7s5hy3je

Average output entropy for quantum channels

Christopher King, David K. Moser
2011 Journal of Mathematical Physics  
We prove equality 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].  ... 
doi:10.1063/1.3658860 fatcat:byjfly6bd5bszgur6aldcb6f7q

Monotonous subsequences and the descent process of invariant random permutations [article]

Mohamed Slim Kammoun
2018 arXiv   pre-print
It is known from the work 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  ... 
arXiv:1805.05253v1 fatcat:x4ccygfej5dnjd5dw6bf7ac4ri

Concentration inequalities for randomly permuted sums [article]

Mélisande Albert
2018 arXiv   pre-print
Initially motivated by the study 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.  ... 
arXiv:1805.03579v1 fatcat:i4powfjq2valviltnj7c4fuvay

A central limit theorem for the number of descents and some urn models [article]

Olivier Garet
2021 arXiv   pre-print
The purpose 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 3β > 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) .  ... 
arXiv:1906.02980v3 fatcat:bk7tcu3jhfadvlqhbb2clry3sm

Bounds on the diameter of Cayley graphs of the symmetric group [article]

John Bamberg, Nick Gill, Thomas Hayes, Harald Helfgott, Ákos Seress, Pablo Spiga
2012 arXiv   pre-print
We prove this conjecture for sets 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.  ... 
arXiv:1205.1596v1 fatcat:ybsspxooqzgwhj4bmie4qmii34

Iteratively Changing the Heights of Automorphism Towers

Gunter Fuchs, Philipp Lücke
2012 Notre Dame Journal of Formal Logic  
We extend the results 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 .  ... 
doi:10.1215/00294527-1715662 fatcat:c4qyj3mp7fembel2nvxtzzhsca

Mathematical structure of magnons in quantum ferromagnets

T Michoel, A Verbeure
1999 Journal of Physics A: Mathematical and General  
We provide the mathematical structure 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 −2βh lim S→∞ ω(F + S (q)F − S (q)) and lim S→∞ ω(F + S (q)F − S (q)) = ω(F + (q)F − (q)).  ... 
doi:10.1088/0305-4470/32/32/303 fatcat:jqgzoc5k6bbudj2vvsoq2nkptu

The length of the longest common subsequence of two independent mallows permutations

Ke Jin
2019 The Annals of Applied Probability  
Since 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 , δe −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  ... 
doi:10.1214/17-aap1351 fatcat:ecghroq6tvffnn3irpvntyphri

A Generalization of the Erdős–Turán Law for the Order of Random Permutation

ALEXANDER GNEDIN, ALEXANDER IKSANOV, ALEXANDER MARYNYCH
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.  ... 
doi:10.1017/s0963548312000247 fatcat:32hyffx2ijhihlklvuvxbsanaa

Bounds on the diameter of Cayley graphs of the symmetric group

John Bamberg, Nick Gill, Thomas P. Hayes, Harald A. Helfgott, Ákos Seress, Pablo Spiga
2013 Journal of Algebraic Combinatorics  
We prove this conjecture for sets 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.  ... 
doi:10.1007/s10801-013-0476-3 fatcat:zrmri62a2fhilkfpowdckl3ooq

Intervals of permutation class growth rates [article]

David Bevan
2015 arXiv   pre-print
We prove that the set 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.  ... 
arXiv:1410.3679v2 fatcat:7i5poymeqvg35dyjv3pcbj7rym
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