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1. Double bubbles on the line with log-convex density f with (logf)′ bounded

   Sothanaphan, Nat ( January 2018 , Missouri journal of mathematical sciences)

   We extend results of Bongiovanni et al. [1] on double bubbles on the line with log-convex density to the case where the derivative of the log of the density is bounded. We show that the tie function between the double interval and the triple interval still exists, but may blow up to infinity in finite time. For the first time, a density is presented for which the blowup time is positive and finite. 

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2. Bruhat Interval Polytopes, 1-Skeleton Lattices, and Smooth Torus Orbit Closures; The Distribution of Descents on Nonnesting Permutations; Pop, Crackle, Snap; Studying Triangulations of Even-Dimensional Cyclic Polytopes via Directed Graphs; Bijections between Planar Maps and Planar Linear Normal λ-Terms with Connectivity Condition; An Algebraic Perspective on Ramsey Numbers; Faces of Directed Edge Polytopes; On the Topology of Cut Complexes of Graphs; An SL4-Web Basis from Hourglass Plabic Graphs; The Associative-Commutative Spectrum of a Binary Operation; Automorphisms of Undirected Bruhat Graphs; Extremal Tensor Products of Demazure Crystals are Direct Sums of Demazure Crystals; Effective Algebraicity for Solutions of Systems of Functional Equations with one Catalytic Variable; Volume Rigidity and Algebraic Shifting; Invariant Theory for the Free Left-Regular Band and a q-Analogue; Rowmotion on 321-Avoiding Permutations; Sums of Weighted Lattice Points of Polytopes; Noncrossing Partitions of an Annulus; Triangular-Grid Billiards and Plabic Graphs; Promotion for Fans of Dyck Paths; Deficit and; Combinatorial Formulas for Shifted Dual Stable Grothendieck Polynomials; Tautological Classes of Matroids; A Realization of Poset Associahedra; Chromatic Quasisymmetric Functions and Noncommutative P-symmetric Functions; Compact Hyperbolic Coxeter d-Polytopes with d+4 Facets and Related Dimension Bounds; Balanced Shifted Tableaux; The Tropical Critical Points of an Affine Matroid; Barrett-Johnson Inequalities for Totally Nonnegative Matrices; From Kreweras to Gessel: A Walk through Patterns in the Quarter Plane; Refined Canonical Stable Grothendieck Polynomials and Their Duals; Quasisymmetric Harmonics of the Exterior Algebra;;; Jack Characters as Generating Series of Bipartite Maps and Proof of Lassalle's Conjecture; Limit Shapes for Skew Howe Duality; Hilbert-Poincaré Series of Matroid Chow Rings and Intersection Cohomology; A Murnaghan-Nakayama Rule for Quantum Cohomology of the Flag Manifold; On the A2 Andrews-Schilling-Warnaar Identities; Hook Length Bias in Odd versus Distinct Partitions; Horizontal-Strip LLT Polynomials; Cyclic Shuffle-Compatibility and Cyclic Quasisymmetric Functions; Set-Valued Tableaux for Macdonald Polynomials; Inequalities for $f^*$-vectors of Lattice Polytopes; Degenerations of the Grassmannian via Matroidal Subdivisions of the Hypersimplex; Castelnuovo-Mumford Regularity for 321-Avoiding Kazhdan-Lusztig Varieties; The Algebra of Extended Peaks; The BCFW Tiling of the Amplituhedron; Pizza and 2-Structures; Robertson's Conjecture in Algebraic Topology; Birational Rowmotion over Noncommutative Rings; Wreath Macdonald Operators; The Isomorphism Problem for Cominuscule Schubert Varieties; 0-Hecke Modules, Quasisymmetric Functions, and Peak Functions in Type B; Modules of the 0-Hecke Algebras for Genomic Schur Functions; Minimal Skew Semistandard Young Tableaux and the Hillman-Grassl Correspondence; Stable-Limit Non-Symmetric Macdonald Functions in Type A; Divisors, Orbit Harmonics, and DT Invariants; Acyclic Pipe Dreams, Subword Complexes and Lattice Quotients of Weak Order Intervals; A Combinatorial Interpretation of the Noncommutative Inverse Kostka Matrix; Polyhedral and Tropical Geometry of Flag Positroids; A new Perspective on Positivity in; Fine Polyhedral Adjunction Theory; Generic Curves and Non-Coprime Catalans; Partial Permutohedra; A Cocharge Formula for the Δ-Springer Modules; Shifted key polynomials; Chainlink Polytopes; Combinatorial Interpretations of the Macdonald Identities for Affine Root Systems; Alternating Sign Matrices and Descending Plane Partitions: a Linear Number of Equivalent Statistics; The Multispecies Zero Range Process and Modified Macdonald Polynomials; A Generalized RSK for Enumerating Linear Series on n-pointed Curves; A Unipotent Realization of the Chromatic Quasisymmetric Function; A Pipe Dream Perspective on Totally Symmetric Self-Complementary Plane Partitions; An Embedding of the Skein Action on Set Partitions into the Skein Action on Matchings; Recursions and Proofs in Cataland; Polyhedral Models for K-Theory of Toric and Flag Varieties; The Kromatic Symmetric Function: A K-Theoretic Analogue of XG; Foata-Like Bijections and science Fiction; Double Dimers and Super Ptolemy Relations; Generalized Pitman-Stanley Flow Polytopes; On Linear Intervals in the alt ν-Tamari Lattices; RSK for 3-Free Posets; Towards Butler's Conjecture; Semistandard Parking Functions and a Finite Shuffle Theorem; A Catalanimal Formula for Macdonald Polynomials; Combinatorial Invariance for Lower Intervals Using Hypercube Decompositions; Equivariant Log-Concavity of Independence Sequences of Claw-Free Graphs; Stembridge Codes and Chow Rings; Interpolating between Classic and Bumpless Pipe Dreams; Rigorous Analytic Combinatorics in Several Variables in SageMath; A Bijectionist's Toolkit

   Christian Gaetz ; Sergi Elizalde ; Colin Defant and Nathan Williams ; Nicholas J. Williams ; Wenjie Fang ; Jesús A. De Loera and William J. Wesley ; Yasuhide Numata, Yusuke Takahashi ; Margaret Bayer, Mark Denker ; Christian Gaetz, Oliver Pechenik ; Jia Huang and Erkko Lehtonen ; et al ( April 2023 , Séminaire lotharingien de combinatoire)

   Krattenthaler, Christian ; Thibon, Jean-Yves (Ed.)
3. Fully Dynamic Connectivity in $O(\log n(\log\log n)^2)$ Amortized Expected Time

   https://doi.org/10.46298/theoretics.23.6  

   Huang, Shang-En ; Huang, Dawei ; Kopelowitz, Tsvi ; Pettie, Seth ; Thorup, Mikkel ( May 2023 , TheoretiCS)

   Dynamic connectivity is one of the most fundamental problems in dynamic graphalgorithms. We present a randomized Las Vegas dynamic connectivity datastructure with $O(\log n(\log\log n)^2)$ amortized expected update time and$O(\log n/\log\log\log n)$ worst case query time, which comes very close to thecell probe lower bounds of Patrascu and Demaine (2006) and Patrascu and Thorup(2011). 

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4. Fully Dynamic Connectivity in O (log n (log log n ) 2 ) Amortized Expected Time

   https://doi.org/10.1137/1.9781611974782.32  

   Huang, Shang-En ; Huang, Dawei ; Kopelowitz, Tsvi ; Pettie, Seth ( January 2017 , SODA 2017)
5. Projectivity of the moduli space of stable log-varieties and subadditivity of log-Kodaira dimension

   https://doi.org/10.1090/jams/871  

   Kovács, Sándor J ; Patakfalvi, Zsolt ( October 2017 , Journal of the American Mathematical Society)

   null (Ed.)