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Higher order Fourier analysis of multiplicative functions and applications

2016
*
Journal of The American Mathematical Society
*

area of mathematics called

doi:10.1090/jams/857
fatcat:a4g5hq5njbe5letm6wks3b2q6a
*additive**combinatorics*, which is primarily concerned with*linear*patterns such as arithmetic progressions in subsets of integers. ... Models and Complexity • Computational*Number**Theory*• Cryptography and information security • Data*structures*• Database*theory*• Design and analysis of algorithms • Distributed computing ...##
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Page 7957 of Mathematical Reviews Vol. , Issue 2000k
[page]

2000
*
Mathematical Reviews
*

(English summary)
Combinatorica 17 (1997), no. 4, 447-458.
2000k:52015b 52C10 51A25
Elekes, Gyorgy (H-EOTVO-C; Budapest)

*On**linear**combinatorics*.*II*.*Structure**theorems**via**additive**number**theory*. ... Although the main slant is al- gorithmic,*structural*results are discussed, such as relations to the general*theory*of valuations*on*polyhedra and connections with the*theory*of toric varieties. ...##
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Page 4571 of Mathematical Reviews Vol. , Issue 96h
[page]

1996
*
Mathematical Reviews
*

We use these

*theorems*to describe a wide class of sequences u (‘*linear*sequences’) for which Ex(u,n) = O(n). Both*theorems*are used for obtaining new superlinear upper bounds as well. ... Hall that encodes,*via**structure*constants known as Hall polynomials, data regarding the lattice of subgroups of a finite abelian p-group (or more generally, modules over a discrete valuation ring with ...##
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Page 6775 of Mathematical Reviews Vol. , Issue 98K
[page]

1998
*
Mathematical Reviews
*

The lower bound is then established by examples of

*additive**linear*orders*on*{1,0,—1} that exhibit worst- case failures of cancellation. N. ... Murray Hill, NJ Failure of cancellation conditions for*additive**linear*orders. ...##
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Page 6609 of Mathematical Reviews Vol. , Issue 99j
[page]

1999
*
Mathematical Reviews
*

*On*combining these results with the main

*theorem*of G. Ding et al. [J. Combin.

*Theory*Ser. ... Specific examples of pitch tournaments are exhibited and several

*theorems*that provide constructions for many

*additional*pitch tournaments are proven. ...

##
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Page 8506 of Mathematical Reviews Vol. , Issue 2004k
[page]

2004
*
Mathematical Reviews
*

Mark Kayll (1-MT; Missoula, MT)

*COMBINATORICS*2004k:05199 05D05 05A16 Chang, Mei-Chu (1-CAR; Riverside, CA)*On*sums and products of distinct*numbers*. (English summary) J. Combin.*Theory*Ser. ... Discrete Math. 16 (2002), no. 1, 99-113 (electronic); MR 2004b:05140] has asymptotically com- puted (*via**linear*programming) size Ramsey*numbers*involving complete bipartite graphs. ...##
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Skew Howe duality and random rectangular Young tableaux

2018
*
Algebraic Combinatorics
*

with the property that the probability distribution

doi:10.5802/alco.8
fatcat:ybio3bsicbb23kddvlnkqokobi
*on*the set of paths of this random walk can be identified (*via*some hypothetical analogue of*Theorem*1.4) with the uniform distribution*on*the set of ... Algebraic*Combinatorics*, Vol. 1 #1 (2018)*Theorem*1.1. ... For more*on*this topic see the work of Sevak Mkrtchyan [11] . Algebraic*Combinatorics*, Vol. 1 #1 (2018) ...##
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On Stochastic Rewriting and Combinatorics via Rule-Algebraic Methods

2021
*
Electronic Proceedings in Theoretical Computer Science
*

*via*pattern-counting observables. ... discrete-time Markov chains and certain types of generating function expressions in

*combinatorics*. ... However, in the

*theory*of Markov chains [23] and in particular in the

*theory*of enumerative

*combinatorics*[19] , even though graph-like

*structures*and their manipulations play a prominent role, it is ...

##
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Page 4442 of Mathematical Reviews Vol. , Issue 2001G
[page]

2001
*
Mathematical Reviews
*

For proving

*Theorem*2, the analytic technique (exponential sums) of Freiman, Low and Pitman, originating in Freiman’s work [Foundations of a*structural**theory*of set*addition*, Translated from the Russian ... Tucker, Applied*combinatorics*, Third edition, Wiley, New York, 1995; MR 95d:05002], the author 11*NUMBER**THEORY*4442 considers sets defined as follows. Let n,d be integers, n > d > 1. ...##
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AMS Fall Western Sectional Sampler

2017
*
Notices of the American Mathematical Society
*

coincides with the

doi:10.1090/noti1591
fatcat:ob7y4bfa7fh7zg5j3rsoyms6eu
*one*pulled back*via*. ... It is well known that studying the representation*theory*of various algebraic*structures*is a rich source for unifying a*number*of parts of mathematics. ...##
###
Page 4882 of Mathematical Reviews Vol. , Issue 84m
[page]

1984
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Mathematical Reviews
*

High points of the book are Hausdorff’s

*structure**theory*for scattered orderings, Laver’s proof of Fraissé’s conjecture for countable orderings, Rubin’s*theorem**on**numbers*of countable models of*theories*... The book divides into four parts: first a short part*on*introductory set*theory*; second a discussion of the*combinatorics*of orderings; third the model*theory*of “pure” countable orderings; and finally ...##
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Book Review: Handbook of enumerative combinatorics

2017
*
Bulletin of the American Mathematical Society
*

*Additive*

*combinatorics*studies

*structures*and extremal properties of sets, such as the set A + B := {x + y : x ∈ A, y ∈ B}. ... These

*structures*are featured in Chapters 11 and 14 of the Handbook of Enumerative

*Combinatorics*. ...

##
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Page 3017 of Mathematical Reviews Vol. , Issue 84h
[page]

1984
*
Mathematical Reviews
*

Chapter XI: Problems of higher connectivity: cut set lattices, many

*theorems*by Mader and others*on**structural*properties of n-connected and n-edge-connected graphs. ... An appendix treats some new developments and*additions*to the main text: Thomassen’s proof of Kuratowski’s*theorem*, hypergraphs, a*theorem*by Voss*on*n-connected graphs with bounded cycle length, the Ulam ...##
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A combinatorial approach to diffeomorphism invariant quantum gauge theories

1997
*
Journal of Mathematical Physics
*

We construct a quantum model from the set of piecewise

doi:10.1063/1.532159
fatcat:mau4xqrmjbcjxl6e422hj7ow6u
*linear*graphs*on*a piecewise*linear*manifold, and another manifestly combinatorial model from graphs defined*on*a sequence of increasingly refined ... Quantum gauge*theory*in the connection representation uses functions of holonomies as configuration observables. ...*II*. ...##
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Page 6100 of Mathematical Reviews Vol. , Issue 87k
[page]

1987
*
Mathematical Reviews
*

Chapter 5 (Crapo) provides an introduction to the approach

*via*combinatorial geometries with special emphasis*on*the role of orthogonality. Chapter 6 (J. ... Daniel Turztk (Prague) 87k:05050 87k:05051 Marcu, Danut (R-BUCH) 87k:05052 A note*on*the independence*number*of an identically self-dual perfect matroid design. Publ. Inst. Math. ...
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