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Factorizations of large cycles in the symmetric group

Dominique Poulalhon, Gilles Schaeffer
2002 Discrete Mathematics  
The factorizations of an n-cycle of the symmetric group Sn into m permutations with prescribed cycle types 1; : : : ; m describe topological equivalence classes of one pole meromorphic functions on Riemann  ...  Our results rely on combining classical methods of the theory of characters of the symmetric group with a combinatorial approach that was ÿrst introduced in the much simpler case m = 2 by Goupil and Schae  ...  Observe that factorizations of an n-cycle are necessarily transitive, since the factorized cycle belongs to the group generated by the factors.  ... 
doi:10.1016/s0012-365x(01)00361-2 fatcat:yeummsfaevhazamiu2koskcczy

Permutation Orbifolds in the large N Limit [article]

Alexandre Belin, Christoph A. Keller, Alexander Maloney
2015 arXiv   pre-print
We also discuss under what conditions the correlation functions factorize at large N and thus reduce to those of a generalized free field in AdS.  ...  In our constructions the spectrum remains finite at large N, but differs qualitatively from that of symmetric orbifolds.  ...  We expect that this projection will eliminate most of the states in (56), since for a g with so many short cycles, the centralizer group is very large.  ... 
arXiv:1509.01256v1 fatcat:4dbudcxcvjabjfthov7rbwaneq

Symmetrical women have higher potential fertility

Grazyna Jasienska, Susan F. Lipson, Peter T. Ellison, Inger Thune, Anna Ziomkiewicz
2006 Evolution and human behavior  
Among urban women, mid-cycle levels of estradiol were 28% higher in the symmetrical group than in the asymmetrical group.  ...  We show that women who are more symmetrical, as assessed by the degree of inequality in the fourth-digit length of their right and left hands, have 13% higher average levels of estradiol over the menstrual  ...  Jozef Puchala of the Jurkow Parish in Poland.  ... 
doi:10.1016/j.evolhumbehav.2006.01.001 fatcat:5iyyydmitfa55jqmqyeh45nyb4

Almost all quasigroups have rank 2

Peter J. Cameron
1992 Discrete Mathematics  
It is shown that, for almost a11 quasigroups Q, the multiplication group Mlt(Q) is symmetric or alternating.  ...  However, the comparative slowness of divergence of the infinite product in this section suggests that the conjecture is fairly delicate.  ...  This conjecture would immediately imply the theorem of this paper.  ... 
doi:10.1016/0012-365x(92)90537-p fatcat:vr42dpzmxzddndpq5qijjpelkm

Wilson Loops in 5d $${\mathcal{N} = 1}$$ SCFTs and AdS/CFT

Benjamin Assel, John Estes, Masahito Yamazaki
2013 Annales de l'Institute Henri Poincare. Physique theorique  
We find agreement in the leading large N limit for a rather general class of representations, including fundamental, anti-symmetric and symmetric representations.  ...  The large N limit of the vacuum expectation values of Wilson loops are computed both by localization in the field theory and by evaluating the fundamental string and D4-brane actions in the dual massive  ...  ,A kq = exp 4π nN 2(8 − N f ) N q a=1 1 − 1 − k a N 3/2 , (1.9) where the Wilson loop is in the k a th anti-symmetric representation for the ath gauge group factor and q is the total number of gauge group  ... 
doi:10.1007/s00023-013-0249-5 fatcat:3udd5wgx4bg5featdk7a5j4l2q

Large Galois groups with applications to Zariski density [article]

Igor Rivin
2015 arXiv   pre-print
for arbitrary polynomials of degree n means the full symmetric group S_n, while for reciprocal polynomials of degree 2n it means the hyperoctahedral group C_2 S_n.).  ...  However, we restrict to the case of the special linear and symplectic groups and rational coefficients in the interest of clarity.  ...  A much simpler deterministic algorithm to check if the Galois group of a monic polynomial of degree d in Z[x] is large (either the symmetric group S d or the alternating group A d ) was discovered by the  ... 
arXiv:1312.3009v4 fatcat:x7jln4qsjva43a6n76slnqula4

The Irreducible Representations of the Symmetric Group

F. D. Murnaghan
1937 Proceedings of the National Academy of Sciences of the United States of America  
,K-P)a' where a' is the class of the symmetric group on n -p letters containing one less cycle on p letters than the corresponding class a of the symmetric group on n letters.  ...  In the present note I state certain theorems on the irreducible representations of the symmetric group in the hope that they may lighten the labors of those carrying out theoretical investigations in nuclear  ... 
doi:10.1073/pnas.23.5.277 pmid:16577772 pmcid:PMC1076920 fatcat:i4uajem4efhtbfm5omr774r7jm

The Group Theoretic Roots of Information: permutations, symmetry, and entropy [article]

David J. Galas
2019 arXiv   pre-print
The harmonic numbers have a well-known combinatorial meaning as the expected number of disjoint, non-empty cycles in permutations of n objects, and since integer entropy is defined in terms of the expected  ...  It is shown that the integer entropy converges uniformly to the Shannon entropy when the group includes all permutations, the Symmetric group, and the number of objects increases without bound.  ...  This work was supported in part by the Bill and Melinda Gates Foundation, the NIH (5U01HL126496), and the Pacific Northwest Research Institute.  ... 
arXiv:1908.09642v2 fatcat:mps4tlibsbgdfbnpmewm6sadly

On the symmetry of current probability distributions in jump processes

A C Barato, R Chetrite
2012 Journal of Physics A: Mathematical and Theoretical  
We study the symmetry of large deviation functions associated with time-integrated currents in Markov pure jump processes.  ...  This condition is related to degeneracies in the set of increments associated with fundamental cycles from Schnakenberg network theory.  ...  We also thank Boris Lander and David Abreu for carefully reading the manunscript. ACB is thankful to the Laboratoire J. A. Dieudonné for hospitality.  ... 
doi:10.1088/1751-8113/45/48/485002 fatcat:xfddczd56zgr7cof27rpszvfzi

Symmetric generating set of the groupsA2n+1andS2n+1usingSnand an element of order two

A. M. Hammas
1998 International Journal of Mathematics and Mathematical Sciences  
In this paper we will show how to generate in generalA2n+1andS2n+1using a copy ofSnand an element of order2inA2n+1orS2n+1for all positive integersn≥2.  ...  We will also show how to generateA2n+1andS2n+1symmetrically usingnelements each of order2.  ...  Let S n be the normalizer of the set F in G, which is a copy of the symmetric group of degree n.  ... 
doi:10.1155/s0161171298000180 fatcat:wsetwa4jjzcv5kndwsnpmdkxu4

A combinatorial model for reversible rational maps over finite fields

John A G Roberts, Franco Vivaldi
2009 Nonlinearity  
cycle lengths of the reduced map in the large field limit (J.  ...  This model also explains the experimental observation that, asymptotically, almost all cycles are symmetrical, and that the probability of occurrence of repeated periods is governed by a Poisson law.  ...  JAGR and FV would like to thank, respectively, the School of Mathematical Sciences at Queen Mary, University of London, and the School of Mathematics and Statistics at the University of New South Wales  ... 
doi:10.1088/0951-7715/22/8/011 fatcat:om7h5mmmevdxdkzbyszynnethq

Possible orders of two generators of the alternating and of the symmetric group

G. A. Miller
1928 Transactions of the American Mathematical Society  
It is well known that every alternating and every symmetric group can be generated by two of its substitutions, and that two such generating substitutions can usually be selected in a large number of different  ...  can be thus generated is the symmetric group of order 6.  ...  of the symmetric group in which it appears.  ... 
doi:10.1090/s0002-9947-1928-1501419-9 fatcat:bxcxq75qjvhchgy3gasib6u2ve

Large Deviations and Moments for the Euler Characteristic of a Random Surface [article]

Kevin Fleming, Nicholas Pippenger
2009 arXiv   pre-print
We obtain large-deviations bounds for the number of cycles that, together with Gamburd's result, allow us to derive sharp estimates for the moments of the number of cycles.  ...  The Euler characteristic of the resulting surface is related to the number of cycles in a certain random permutation of {1, ..., N}.  ...  Note that definitions of the cycle indicator differ among these authors by a factor of the order of the group, in this case l!).  ... 
arXiv:0902.3646v1 fatcat:4srpwvbvovgrjamq4kyl5poaje

Sub-Shimura Varieties for type O(2,n)

Andrew Fiori
2018 Journal de Théorie des Nombres de Bordeaux  
We give a classification, up to consideration of component groups, of sub-Shimura varieties of those Shimura Varieties attached to orthogonal groups of signature (2,n) over Q.  ...  Acknowledgments The author would like to thank Prof. Eyal Goren for suggesting the problem studied in this paper.  ...  They would also like to thank Majid Shahabi for their help in proofreading this article.  ... 
doi:10.5802/jtnb.1060 fatcat:4dadbpfc7vgltl4dzf7tbunolu

The Topological Symmetric Orbifold [article]

Songyuan Li, Jan Troost
2020 arXiv   pre-print
Moreover, it allows to leverage results on the combinatorics of the symmetric group to compute more structure constants explicitly.  ...  Indeed, we propose a concrete mathematical incarnation of the proof, relating Gromow-Witten theory in the bulk to the quantum cohomology of the Hilbert scheme on the boundary.  ...  The symmetric group acts on the tensor product factors and the action takes into account the grading of the factors.  ... 
arXiv:2006.09346v2 fatcat:7pwl6z54g5g6jgdsskyihhhnry
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