Hypergraphs with infinitely many extremal constructions by Jianfeng Hou, Heng Li, Xizhi Liu, Dhruv Mubayi, Yixiao Zhang

“…This is one of the most famous open problems in extremal combinatorics. It is conjectured that the extremal density is 5/9, but a sign that the conjecture is hard is that if the conjecture is true, the example just presented is not _the_ extremal example, but merely _an_ extremal example, as it is now known that there is an infinite family of 3-uniform hypergraphs with no cliques of size 4 and with asymptotic density 5/9. …”
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The Singularity of the <i>K</i>₄ Homeomorphic Graph by Haicheng Ma

“…The singularity of graphs is of certain interest in graph theory and algebraic combinatorics. For positive integers <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>a</mi><mi>i</mi></msub><mo>≥</mo><mn>2</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>…</mo><mo>,</mo><mn>6</mn></mrow></semantics></math></inline-formula>. …”
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Geometric rank of tensors and subrank of matrix multiplication by Swastik Kopparty, Guy Moshkovitz, Jeroen Zuiddam

“…Since this paper first appeared as a preprint, the notion of geometric rank has played an important role in a central problem of additive combinatorics, which is to relate analytic rank to partition rank (where the rank-1 tensors of degree $d$ are those of the form $UV$, where $U$ and $V$ depend on disjoint sets of variables). …”
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Gowers norms for automatic sequences by Jakub Byszewski, Jakub Konieczny, Clemens Müllner

“…There are several situations in additive and extremal combinatorics where it is useful to decompose an object $X$ into a "structured" part $S(X)$ and a "quasirandom" part $Q(X)$. …”
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Failure of the trilinear operator space Grothendieck theorem by Jop Briët, Carlos Palazuelos

“…Interestingly, and very appropriately for a paper in Discrete Analysis, the proof makes use of ideas from additive combinatorics. In particular, it makes use of a noncommutative version of the generalized von Neumann inequality. …”
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Efficient arithmetic regularity and removal lemmas for induced bipartite patterns by Noga Alon, Jacob Fox, Yufei Zhao

“…In addition to Haussler's packing lemma, a by now standard tool in the setting of bounded VC-dimension, the proof uses the celebrated Bogolyubov-Ruzsa lemma from additive combinatorics, which, in the context of a finite abelian group $G$ of bounded exponent, states that the iterated sum set $2B-2B$ of a set $B$ with small doubling contains a subgroup of $G$ of size at least a constant times $|B|$. …”
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Punctured Low-Bias Codes Behave Like Random Linear Codes by Venkatesan Guruswami, Jonathan Mosheiff

“…Another is to use an approach that is now very standard in probabilistic combinatorics but was much less standard at the time, which is to choose points of $A$ independently at random with a probability that ensures that the expected number of pairs of points at distance $cn$ is less than half the expected size of $A$, after which one can remove a point from each bad pair. …”
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The splitting method and Poincare's theorem: (I) - the geometric part by Maurice Margenstern

“…At the price of a small extension of the definition of a combinatoric tiling, which we call quasi-combinatoric, we show that all tessellations with the above numbers p, q and r are quasi-combinatoric for all possible values of p, q and r, the case when p=2 and q=3 being included. …”
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Robot's hand and expansions in non-integer bases by Paola Loreti, Anna Chiara Lai

“…Combinatorics…”
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Representation type of Hecke algebras of type A by Erdmann, K, Nakano, D

“…In this paper we provide a complete classification of the representation type for the blocks for the Hecke algebra of type A, stated in terms of combinatorical data. The computation of the complexity of Young modules is a key component in the proof of this classification result.…”

Notes on the Hodge conjecture for Fermat varieties by Genival da Silva, Adrian Clingher

“…We review a combinatoric approach to the Hodge conjecture for Fermat varieties and announce new cases where the conjecture is true. …”
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Search for charmless hadronic decays of B mesons with the SLAC SLD detector by Abe, K, Abe, K, Abe, T, Adam, I, Akagi, T, Akimoto, H, Allen, N, Ash, W, Aston, D, Baird, K, Baltay, C, Band, H, Barakat, M, Bardon, O, Barklow, T, Bashindzhagyan, G, Bauer, J, Bellodi, G, Benvenuti, A, Bilei, G, Bisello, D, Blaylock, G, Bogart, JR, Bower, G, Brau, J

“…The precise tracking capabilities of the SLD detector provided for the efficient reduction of combinatoric backgrounds, yielding the most precise available limits for ten of these modes.…”

Multiword expressions : a pain in the neck for NLP by Sag, Ivan A., Baldwin, Timothy, Bond, Francis, Copestake, Ann, Flickinger, Dan

“…The various kinds of multiword expressions should be analyzed in distinct ways, including listing “words with spaces”, hierarchically organized lexicons, restricted combinatoric rules, lexical selection, “idiomatic constructions” and simple statistical affinity. …”
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Methods for Parallelizing Search Paths in Phrasing by Marcken, Carl de

“…Many search problems are commonly solved with combinatoric algorithms that unnecessarily duplicate and serialize work at considerable computational expense. …”
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Matera in Many Dimensions by Sandra Lucente

“…We reach this objective by using a combinatoric puzzle and suitable story telling.…”
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The splitting method and Poincare's theorem: (II) - matrix, polynomial and language by Maurice Margenstern

“…This new part is also based on the definition of a combinatoric tiling which was detailed in the previous issue. …”
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The effect of Al on the corrosion resistance of binary Mg-Al solid solutions: Combining in-situ electrochemistry with combinatorial thin films by Markus Felten, Alexander Lutz, Shamsa Aliramaji, Siyuan Zhang, Christina Scheu, Jochen Schneider, Daniela Zander

“…These spatially resolving characterization techniques are employed along the Al concentration gradient of the combinatorically grown thin films enabling efficient screening of the Al concentration dependent electrochemical corrosion behaviour. …”
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Conversion in poetic communication of Afanasy Fet’s lyric poetry by Bezrukov Andrei Nikolayevich

“…In conclusion, the poetic discourse combinatorically connects different facets of language realization which forms semantic variety of lyrics and unordinary nature of the reader's reception.…”
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Navigability, Walkability, and Perspicacity Associated with Canonical Ensembles of Walks in Finite Connected Undirected Graphs—Toward Information Graph Theory by Dimitri Volchenkov

“…The application of information theory methods to problems about graphs, in contrast to geometric, combinatoric, algorithmic, and algebraic approaches, can be called information graph theory. …”
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Interaction and Depth against Nondeterminism in Proof Search by Ozan Kahramanogullari

“…Deep inference provides more freedom in the design of deductive systems for different logics and a rich combinatoric analysis of proofs. In particular, construction of exponentially shorter analytic proofs becomes possible, however with the cost of a greater nondeterminism than in the sequent calculus. …”
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