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Higher order Fourier analysis of multiplicative functions and applications

Nikos Frantzikinakis, Bernard Host
2016 Journal of The American Mathematical Society  
area of mathematics called 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  ... 
doi:10.1090/jams/857 fatcat:a4g5hq5njbe5letm6wks3b2q6a

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.  ... 

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  ... 

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.  ... 

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.  ... 

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.  ... 

Skew Howe duality and random rectangular Young tableaux

Greta Panova, Piotr Śniady
2018 Algebraic Combinatorics  
with the property that the probability distribution 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)  ... 
doi:10.5802/alco.8 fatcat:ybio3bsicbb23kddvlnkqokobi

On Stochastic Rewriting and Combinatorics via Rule-Algebraic Methods

Nicolas Behr
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  ... 
doi:10.4204/eptcs.334.2 fatcat:beepbbvpfbcjdbzvn6dnguekoa

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.  ... 

AMS Fall Western Sectional Sampler

Pavel Etingof, Monica Vazirani, Paul Balmer
2017 Notices of the American Mathematical Society  
coincides with the 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.  ... 
doi:10.1090/noti1591 fatcat:ob7y4bfa7fh7zg5j3rsoyms6eu

Page 4882 of Mathematical Reviews Vol. , Issue 84m [page]

1984 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  ... 

Book Review: Handbook of enumerative combinatorics

Robin Pemantle
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.  ... 
doi:10.1090/bull/1607 fatcat:j6cl36orsvcvtdw4k5nylh34he

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  ... 

A combinatorial approach to diffeomorphism invariant quantum gauge theories

José A. Zapata
1997 Journal of Mathematical Physics  
We construct a quantum model from the set of piecewise 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.  ... 
doi:10.1063/1.532159 fatcat:mau4xqrmjbcjxl6e422hj7ow6u

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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