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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
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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. ...
doi:10.1016/0097-3165(74)90076-4
fatcat:z3yb6hc47feavo4ssqk4vjmgni
Page 1026 of Mathematical Reviews Vol. 48, Issue 4
[page]
1974
Mathematical Reviews
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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
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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 ...
doi:10.1080/00029890.1949.11999421
fatcat:mpioq45llbhnznld2k4kknhovm
The matching, birthday and the strong birthday problem: a contemporary review
2005
Journal of Statistical Planning and Inference
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This article provides 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. ...
doi:10.1016/j.jspi.2003.11.015
fatcat:b7bri4btgjgvllh2xtw4lib4hm
A survey of known results and research areas for n-queens
2009
Discrete Mathematics
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We then investigate 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. ...
doi:10.1016/j.disc.2007.12.043
fatcat:zvfp2vjgqnb5fcwjd4ruf5ufne
Majorization and Rényi Entropy Inequalities via Sperner Theory
[article]
2018
arXiv
pre-print
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It is then used 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. ...
arXiv:1712.00913v3
fatcat:zrlub7zupbhw3ke4rqmjuropxa
Enumerative and Algebraic Combinatorics in the 1960's and 1970's
[article]
2021
arXiv
pre-print
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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] . ...
arXiv:2105.07884v3
fatcat:f332bkdpsjhprnjowgjceylvpi
Probabilistic Bounds on the Coefficients of Polynomials with Only Real Zeros
1997
Journal of combinatorial theory. Series A
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Such sequences (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 ...
doi:10.1006/jcta.1997.2747
fatcat:p4xe7kf5urbhzd5gowacwjw3rm
Independent Process Approximations for Random Combinatorial Structures
1994
Advances in Mathematics
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DEDICATED 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. ...
doi:10.1006/aima.1994.1022
fatcat:tvrixmob3bbznmdpu65tgnattu
On zonotopes
1971
Transactions of the American Mathematical Society
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In this paper is described 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. ...
doi:10.1090/s0002-9947-1971-0279689-2
fatcat:gxxhgm5wtnbwnktm6eokvrh4wm
On Zonotopes
1971
Transactions of the American Mathematical Society
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In this paper is described 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. ...
doi:10.2307/1996000
fatcat:iwr4s2istreojmawpr3buqiphe
Powers of staircase Schur functions and symmetric analogues of Bessel polynomials
1996
Discrete Mathematics
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This leads 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. ...
doi:10.1016/0012-365x(95)00138-m
fatcat:vvhabu5zf5brflg5uuw2bp7434
Independent Process Approximations for Random Combinatorial Structures
[article]
2013
arXiv
pre-print
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Many random combinatorial objects have 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. ...
arXiv:1308.3279v1
fatcat:l34iglvhwfbnxjnouiqvikmjyq
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.)
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In presenting this thesis in partial fulfilment 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 ...
doi:10.1080/00220671.1980.10885223
fatcat:ii3smamiefadfam2zqfa5fj76e
Paley and the Paley graphs
[article]
2017
arXiv
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This paper discusses some aspects 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. ...
arXiv:1702.00285v1
fatcat:d6kuccqyrzanjhavjkardxoho4
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