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Journal of Combinatorial Theory, Series B, ISSN 0095-8956, 11/2015, Volume 115, pp. 186 - 209
In a break-through paper, Lovász [20] determined the chromatic number of Kneser graphs. This was improved by Schrijver [27], by introducing the Schrijver... 
[formula omitted]-Tucker lemma | Kneser hypergraphs | Tucker–Ky Fan's lemma | Chromatic number | Tucker-Ky Fan's lemma | Tucker lemma | MATHEMATICS | PROOF | Z(p)-Tucker lemma | GRAPHS | Computer science
Journal Article
02/2019, ISBN 9780691181387, 281
Outer billiards provides a toy model for planetary motion and exhibits intricate and mysterious behavior even for seemingly simple examples. It is a dynamical... 
Mathematics | Combinatorial number theory
eBook
Advances in mathematics (New York. 1965), ISSN 0001-8708, 2014, Volume 256, pp. 206 - 290
Szemerédi's regularity lemma is a fundamental tool in extremal combinatorics. However, the original version is only helpful in studying dense graphs. In the... 
Sparse regularity lemma | Szemerédi's regularity lemma | Counting lemma | Graph removal lemma | Extremal combinatorics | Sparse graphs | Szemeredi's regularity lemma | FREQUENCIES | NUMBER | APPROXIMATION | PROOF | REGULARITY LEMMA | RAMSEY | MATHEMATICS | UNIVERSAL GRAPHS | BOUNDS | SUBGRAPHS
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 09/2019, Volume 371, Issue 9, pp. 6169 - 6212
This article gives a proof of the Langlands-Shelstad fundamental lemma for the spherical Hecke algebra for every unramified p-adic reductive group G in large... 
MATHEMATICS | ENDOSCOPY | FUNDAMENTAL LEMMA
Journal Article
Stochastic processes and their applications, ISSN 0304-4149, 2015, Volume 125, Issue 11, pp. 4039 - 4065
Let {Xi(t),t≥0},1≤i≤n be mutually independent centered Gaussian processes with almost surely continuous sample paths. We derive the exact asymptotics of... 
Extremes | Gaussian process | Generalized Piterbarg constant | Conjunction | Borell–TIS inequality | Generalized Pickands constant | Piterbarg inequality | Slepian lemma | Pickands–Piterbarg lemma | Double-sum method | Borell-TIS inequality | Pickands-Piterbarg lemma | INEQUALITIES | CONSTANT | STATISTICS & PROBABILITY | Sects | Analysis | Gaussian processes
Journal Article
Problemy Analiza, ISSN 2306-3424, 2018, Volume 7, Issue 1, pp. 87 - 103
For 0 < λ ≤ 1, let U(λ) denote the family of functions f(z)=... analytic in the unit disk D satisfying the condition |...| < λ in D. Although functions in this... 
Subordination | Univalent function | Julia's lemma | Schwarz' lemma | Univalent function ◆ subordination ◆ Julia’s lemma ◆ Schwarz’ lemma
Journal Article
Random Structures & Algorithms, ISSN 1042-9832, 03/2020, Volume 56, Issue 2, pp. 306 - 338
Advancing the sparse regularity method, we prove one‐sided and two‐sided regularity inheritance lemmas for subgraphs of bijumbled graphs, improving on results... 
Szemerédi's regularity lemma | counting lemma | pseudorandom graphs | sparse regularity lemma | regularity inheritance | Szemeredi's regularity lemma | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS | MATHEMATICS, APPLIED | CONJECTURE | Graphs | Inheritances | Graph theory | Regularity | Pseudorandom
Journal Article
Journal of Algebra, ISSN 0021-8693, 10/2019, Volume 535, pp. 1 - 34
We establish a generalized form both of the Gabriel-Zisman exact sequence associated with a pointed functor between pointed groupoids, and of the Brown exact... 
Fibration | Snail lemma | Snake lemma | Internal groupoid | MATHEMATICS | FIBRATIONS | FRACTIONS | BUTTERFLIES | CATEGORIES | Snakes
Journal Article
Journal of algebra, ISSN 0021-8693, 2013, Volume 383, pp. 197 - 211
Many variations of the notions of clean and strongly clean have been studied by a variety of authors. We develop a general theory, based on idempotents and... 
Clean rings | Fittingʼs Lemma | Fitting's Lemma | MATHEMATICS | MATRIX-RINGS | UNIT | LOCAL-RINGS
Journal Article
International Mathematics Research Notices, ISSN 1073-7928, 11/2018, Volume 2018, Issue 21, pp. 6611 - 6616
Abstract Recently, Wu–Yau and Tosatti–Yang established the connection between the negativity of holomorphic sectional curvatures and the positivity of... 
MATHEMATICS | SCHWARZ LEMMA
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 11/2015, Volume 143, Issue 11, pp. 4713 - 4721
őmaximal sum-free sets there are in \{1, \dots , n\} 2^{\lfloor n/4 \rfloor } 2^{(1/4+o(1))n} . Our proof makes use of container and removal lemmas of Green as... 
MATHEMATICS | MATHEMATICS, APPLIED | LEMMA
Journal Article
Tatra Mountains Mathematical Publications, ISSN 1210-3195, 09/2015, Volume 64, Issue 1, pp. 1 - 19
In this note the usual Goursat lemma, which describes subgroups of the direct product of two groups, is generalized to describing subgroups of a direct product... 
Goursat’s lemma | Goursat's lemma
Journal Article
Theoretical computer science, ISSN 0304-3975, 2015, Volume 597, pp. 1 - 17
•Intensional classical linear logic (MELL) is proved decidable.•Intensional interlinear logic (RLL) is proved decidable.•We adapt Kripke's method used to prove... 
Linear logic | Relevance logic | Decidability | Cognate sequent | Modal logic | Kripke's lemma | Curry's lemma | König's lemma | Sequent calculus | RELEVANT IMPLICATION | Ktinig's lemma | COMPUTER SCIENCE, THEORY & METHODS | MULTISETS | Formulations | Thinning | Mathematical analysis | Proving | Calculus | Logic | Fragmentation
Journal Article
Systems & Control Letters, ISSN 0167-6911, 09/2016, Volume 95, pp. 3 - 10
The Kalman–Yakubovich–Popov lemma is a central result in systems and control theory which relates the positive semidefiniteness of a Popov function on the... 
Popov function | Bounded real lemma | Kalman–Yakubovich–Popov lemma | Differential-algebraic equation | Positive real lemma | Kalman-Yakubovich-Popov lemma | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | RICCATI EQUATION | AUTOMATIC-CONTROL | AUTOMATION & CONTROL SYSTEMS | Control systems | Equality
Journal Article
Journal of the ACM (JACM), ISSN 0004-5411, 09/2019, Volume 66, Issue 5, pp. 1 - 45
Journal Article
Journal of Differential Geometry, ISSN 0022-040X, 2012, Volume 91, Issue 3, pp. 361 - 381
Given a closed Riemannian manifold, we show how to close an orbit of the geodesic flow by a small perturbation of the metric in the C-1 topology. 
MATHEMATICS | LEMMA
Journal Article
Journal de mathématiques pures et appliquées, ISSN 0021-7824, 08/2015, Volume 104, Issue 2, pp. 207 - 226
Let Ω be a domain in RN, i.e., a bounded and connected open subset of RN with a Lipschitz-continuous boundary ∂Ω, the set Ω being locally on the same side of... 
Nečas inequality | Poincaré lemma | J.L. Lions lemma | de Rham theorem | Bogovskii's proof of the surjectivity of the divergence operator | 46E35 | 74B05 | De Rham theorem | 46E05 | JL Lions lemma | Poincare lemma | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | PROOF | Necas inequality | Functional Analysis | Analysis of PDEs | Mathematics
Journal Article
The Journal of geometric analysis, ISSN 1559-002X, 2018, Volume 29, Issue 3, pp. 2469 - 2491
Journal Article
SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2018, Volume 32, Issue 1, pp. 591 - 610
We treat problems of fair division, their various interconnections, and their relations to Sperner's lemma and the Knaster-Kuratowski-Mazurkiewicz (KKM)... 
Sperner’s lemma | Fair division | KKM theorem | Cake cutting | Necklace splitting | Combinatorial fixed point theorems | MATHEMATICS, APPLIED | Sperner's lemma | combinatorial fixed point theorems | LEMMA | PROOF | BISECTION | necklace splitting | cake cutting | DISCRETE | THEOREMS | fair division | PARTITIONS
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 04/2012, Volume 75, Issue 6, pp. 3072 - 3077
A strong compactness result in the spirit of the Lions–Aubin–Simon lemma is proven for piecewise constant functions in time (uτ) with values in a Banach space.... 
Aubin lemma | Rothe method | Compactness
Journal Article
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