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Independent permutations, as related to a problem of Moser and a theorem of Pólya

1974
*
Journal of combinatorial theory. Series A
*

*As*

*a*special case

*of*this treatment we obtain Pblya's

*theorem*that this

*problem*can be solved if

*and*only if n is not

*a*multiple

*of*2 or 3. ...

*Independent*

*permutations*are also

*related*

*to*the

*problem*

*of*placing n noncapturing superqueens (chess queens with wrap-around capability) on an n x n board. ... We also

*relate*

*independent*

*permutations*

*to*

*a*

*problem*posed by

*Moser*[4, 51. ...

##
###
Page 1026 of Mathematical Reviews Vol. 48, Issue 4
[page]

1974
*
Mathematical Reviews
*

Etherington (Edinburgh)
5873
COMBINATORICS 1026
Chandra, Ashok K. 5874

*Independent**permutations*,*as**related**to**a**problem**of**Moser**and**a**theorem**of*Pélya. J. Combinatorial Theory Ser. ...*A*set*of**permutations*{P,, ---, Pa} is said*to*be*independent*if the function F: D,—> D,, defined by F(x) = P;'(x) +--+ + P,'(x) (mod nj is*a**permutation*. ...##
###
Elementary Problems and Solutions

1949
*
The American mathematical monthly
*

*As*

*a*somewhat similar,

*and*perhaps equally difficult, enumera- tion

*problem*we might here mention the following: Let P; be

*a*

*permutation*

*of*n objects. In how many ways can we form

*a*sequence

*of*m! ... starting with the two sequences S,(2) =

*a*, d2, a1

*and*S2(2) =

*a*, a1, a2, even though they are not

*independent*, there are obtained by means

*of*

*relations*(1)

*and*(2) the two

*independent*sequences (3) Si(3 ...

##
###
The matching, birthday and the strong birthday problem: a contemporary review

2005
*
Journal of Statistical Planning and Inference
*

This article provides

doi:10.1016/j.jspi.2003.11.015
fatcat:b7bri4btgjgvllh2xtw4lib4hm
*a*contemporary exposition at*a*moderately quantitative level*of*the distribution theory associated with the matching*and*the birthday*problems*. ...*A*large number*of*examples, many not well known, are provided*to*help*a*reader have*a*feeling for these questions at an intuitive level. ... Acknowledgements It is*a*pleasure*to*thank Jim Pitman*and*Shelley Zacks for their help*and*comments. References Abramson, M.,*Moser*, W., 1970. More birthday surprises. Amer. Math. ...##
###
A survey of known results and research areas for n-queens

2009
*
Discrete Mathematics
*

We then investigate

doi:10.1016/j.disc.2007.12.043
fatcat:zvfp2vjgqnb5fcwjd4ruf5ufne
*a*number*of*open research areas for the*problem*, stating several existing*and*new conjectures. ... In this paper we survey known results for the n-queens*problem**of*placing n nonattacking queens on an n × n chessboard*and*consider extensions*of*the*problem*, e.g. other board topologies*and*dimensions ... Paul Mezo for translating from the German some*of*the earlier work that had been done by Ahrens, Behmann, Günther, Netto, Pauls*and**Pólya*, the paper by Stern,*and*the paper by Schlude*and*Specker, Dr. ...##
###
Majorization and Rényi Entropy Inequalities via Sperner Theory
[article]

2018
*
arXiv
*
pre-print

It is then used

arXiv:1712.00913v3
fatcat:zrlub7zupbhw3ke4rqmjuropxa
*to*obtain*a*variety*of*consequences, including new R\'enyi entropy inequalities for sums*of**independent*, integer-valued random variables. ...*A*natural link between the notions*of*majorization*and*strongly Sperner posets is elucidated. ... Acknowledgments The authors are indebted*to*Manjunath Krishnapur for very useful discussions,*and**to*two anonymous reviewers for detailed*and*constructive comments that greatly improved the exposition. ...##
###
Enumerative and Algebraic Combinatorics in the 1960's and 1970's
[article]

2021
*
arXiv
*
pre-print

*A*partly autobiographical survey

*of*the development

*of*enumerative

*and*algebraic combinatorics in the 1960's

*and*1970's. ... I am grateful

*to*Adriano Garsia, Ming-chang Kang, Igor Pak, Victor Reiner, Christophe Reutenauer

*and*especially Curtis Greene for many helpful suggestions. ...

*of*RSK (

*and*the notion

*of*dual RSK, which for

*permutations*is the same

*as*RSK)

*to*

*permutations*

*of*multisets [76] . ...

##
###
Probabilistic Bounds on the Coefficients of Polynomials with Only Real Zeros

1997
*
Journal of combinatorial theory. Series A
*

Such sequences (

doi:10.1006/jcta.1997.2747
fatcat:p4xe7kf5urbhzd5gowacwjw3rm
*a*0 , ...,*a*n ) are also known*to*be characterized by total positivity*of*the infinite matrix (*a*i& j ) indexed by nonnegative integers i*and*j. ... The work*of*Harper*and*subsequent authors has shown that finite sequences (*a*0 , ...,*a*n ) arising from combinatorial*problems*are often such that the polynomial*A*(z) := n k=0*a*k z k has only real zeros ... INFINITE*POLYA*FREQUENCY SEQUENCES Associate the sequence (*a*0 ,*a*1 , ...) with its generating function*A*(z) := : i=1*a*i z i . ( 52 ) According*to*the result*of*Edrei [33] presented in [74]*as**Theorem*...##
###
Independent Process Approximations for Random Combinatorial Structures

1994
*
Advances in Mathematics
*

DEDICATED

doi:10.1006/aima.1994.1022
fatcat:tvrixmob3bbznmdpu65tgnattu
*TO*THE MEMORY*OF*MARK KAC, WHO SOUGHT OUT*INDEPENDENCE*IN ANALYSIS*AND*NUMBER THEORY Many random combinatorial objects have*a*component structure whose joint distribution is equal*to*that*of*... Among the examples are combinatorial assemblies (e.g.,*permutations*, random mapping functions,*and*partitions*of**a*set), multisets (e.g, polynomials over*a*finite field, mapping patterns*and*partitions ... Notation There are several types*of*asymptotic*relations*used in this paper. For sequences {*a*, }*and*{ b , } , we write*a*,--,, for the asymptotic*relation**a*,/b, + 1*as*n + 00. ...##
###
On zonotopes

1971
*
Transactions of the American Mathematical Society
*

In this paper is described

doi:10.1090/s0002-9947-1971-0279689-2
fatcat:gxxhgm5wtnbwnktm6eokvrh4wm
*a*diagram technique for zonotopes, or vector sums*of*line segments, which is analogous*to*that*of*Gale diagrams for general polytopes,*and*central diagrams for centrally symmetric ... The use*of*these new zonal diagrams leads*to*relationships between zonotopes with n zones*of*dimensions d*and*n -d,*and*enables one*to*enumerate all the combinatorial types*of*dzonotopes with ntsd+2 zones ...*As*before, we deduce from the Corollary*to**Theorem*5*and**Theorem*6*Theorem*8. ...##
###
On Zonotopes

1971
*
Transactions of the American Mathematical Society
*

In this paper is described

doi:10.2307/1996000
fatcat:iwr4s2istreojmawpr3buqiphe
*a*diagram technique for zonotopes, or vector sums*of*line segments, which is analogous*to*that*of*Gale diagrams for general polytopes,*and*central diagrams for centrally symmetric ... The use*of*these new zonal diagrams leads*to*relationships between zonotopes with n zones*of*dimensions d*and*n -d,*and*enables one*to*enumerate all the combinatorial types*of*dzonotopes with ntsd+2 zones ...*As*before, we deduce from the Corollary*to**Theorem*5*and**Theorem*6*Theorem*8. ...##
###
Powers of staircase Schur functions and symmetric analogues of Bessel polynomials

1996
*
Discrete Mathematics
*

This leads

doi:10.1016/0012-365x(95)00138-m
fatcat:vvhabu5zf5brflg5uuw2bp7434
*to**a*new determinantal expression for Bessel polynomials*and*suggests that their combinatorics might be linked*to*Young tableaux or shifted Young tableaux. ... These identities are then interpreted in terms*of**a*sequence*of*orthogonal polynomials in one variable x, with coefficients in the ring*of*symmetric functions. ... Svrtan for pointing out the connection with Korteweg-de-Vries equation*and*kindly providing references on this subject. ...##
###
Independent Process Approximations for Random Combinatorial Structures
[article]

2013
*
arXiv
*
pre-print

Many random combinatorial objects have

arXiv:1308.3279v1
fatcat:l34iglvhwfbnxjnouiqvikmjyq
*a*component structure whose joint distribution is equal*to*that*of**a*process*of*mutually*independent*random variables, conditioned on the value*of**a*weighted sum ... Among the examples are combinatorial assemblies (e.g.*permutations*, random mapping functions,*and*partitions*of**a*set), multisets (e.g. polynomials over*a*finite field, mapping patterns*and*partitions ... Since the refined combinatorial process D(n)*and*the refined*independent*process Y (n) are*related*by conditioning on the value*of**a*weighted sum*of*the Y 's,*Theorem*3 applies. ...##
###
The Effect of Teaching Heuristics on the Ability of Grade Ten Students to Solve Novel Mathematical Problems

1980
*
The Journal of educational research (Washington, D.C.)
*

In presenting this thesis in partial fulfilment

doi:10.1080/00220671.1980.10885223
fatcat:ii3smamiefadfam2zqfa5fj76e
*of*the requirements for an advanced degree at the University*of*British Columbia, I agree that the Library shall make it freely available for reference*and*... I further agree that permission for extensive copying*of*this thesis for scholarly purposes may be granted by the Head*of*my Department or by his representatives. ...*Polya*(1954, p. 32) defined analogy*as*"*a*sort*of*similarity," while Dinsmore (1971, p. 17) defined it "*as*the perception*of**a*similarity between the*problem*,*to*be solved*and*one that has already been ...##
###
Paley and the Paley graphs
[article]

2017
*
arXiv
*
pre-print

This paper discusses some aspects

arXiv:1702.00285v1
fatcat:d6kuccqyrzanjhavjkardxoho4
*of*the history*of*the Paley graphs*and*their automorphism groups. ...*To*be more precise about [14] , the*theorem*Carlitz proved was*as*follows:*Theorem*9.2 If q is*a*power*of*an odd prime p, then any*permutation*polynomial F q → F q , which fixes 0*and*1*and*satisfies ... The first proof*to*do that is the subject*of*the next section. Muzychuk's proof*of*the main*theorem*In 1987 Muzychuk [65]*independently*gave*a*full proof*of**Theorem*9.1. ...
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