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Factorizations of large cycles in the symmetric group

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*. ...

##
###
Permutation Orbifolds in the large N Limit
[article]

2015
*
arXiv
*
pre-print

We also discuss under what conditions

arXiv:1509.01256v1
fatcat:4dbudcxcvjabjfthov7rbwaneq
*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*. ...##
###
Symmetrical women have higher potential fertility

2006
*
Evolution and human behavior
*

Among urban women, mid-

doi:10.1016/j.evolhumbehav.2006.01.001
fatcat:5iyyydmitfa55jqmqyeh45nyb4
*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. ...##
###
Almost all quasigroups have rank 2

1992
*
Discrete Mathematics
*

It is shown that, for almost a11 quasigroups Q,

doi:10.1016/0012-365x(92)90537-p
fatcat:vr42dpzmxzddndpq5qijjpelkm
*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. ...##
###
Wilson Loops in 5d $${\mathcal{N} = 1}$$ SCFTs and AdS/CFT

2013
*
Annales de l'Institute Henri Poincare. Physique theorique
*

We find agreement

doi:10.1007/s00023-013-0249-5
fatcat:3udd5wgx4bg5featdk7a5j4l2q
*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*...##
###
Large Galois groups with applications to Zariski density
[article]

2015
*
arXiv
*
pre-print

for arbitrary polynomials

arXiv:1312.3009v4
fatcat:x7jln4qsjva43a6n76slnqula4
*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*...##
###
The Irreducible Representations of the Symmetric Group

1937
*
Proceedings of the National Academy of Sciences of the United States of America
*

,K-P)a' where a' is

doi:10.1073/pnas.23.5.277
pmid:16577772
pmcid:PMC1076920
fatcat:i4uajem4efhtbfm5omr774r7jm
*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 ...##
###
The Group Theoretic Roots of Information: permutations, symmetry, and entropy
[article]

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. ...

##
###
On the symmetry of current probability distributions in jump processes

2012
*
Journal of Physics A: Mathematical and Theoretical
*

We study

doi:10.1088/1751-8113/45/48/485002
fatcat:xfddczd56zgr7cof27rpszvfzi
*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. ...##
###
Symmetric generating set of the groupsA2n+1andS2n+1usingSnand an element of order two

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. ...

##
###
A combinatorial model for reversible rational maps over finite fields

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 ...

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

1928
*
Transactions of the American Mathematical Society
*

It is well known that every alternating and every

doi:10.1090/s0002-9947-1928-1501419-9
fatcat:bxcxq75qjvhchgy3gasib6u2ve
*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. ...##
###
Large Deviations and Moments for the Euler Characteristic of a Random Surface
[article]

2009
*
arXiv
*
pre-print

We obtain

arXiv:0902.3646v1
fatcat:4srpwvbvovgrjamq4kyl5poaje
*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!). ...##
###
Sub-Shimura Varieties for type O(2,n)

2018
*
Journal de Théorie des Nombres de Bordeaux
*

We give a classification, up to consideration

doi:10.5802/jtnb.1060
fatcat:4dadbpfc7vgltl4dzf7tbunolu
*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. ...##
###
The Topological Symmetric Orbifold
[article]

2020
*
arXiv
*
pre-print

Moreover, it allows to leverage results on

arXiv:2006.09346v2
fatcat:7pwl6z54g5g6jgdsskyihhhnry
*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*. ...
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