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1. To Shuffle or Not To Shuffle: Mini-Batch Shuffling Strategies for Multi-class Imbalanced Classification

   https://doi.org/10.1109/CSCI58124.2022.00057  

   Mao, Yuwei ; Gupta, Vishu ; Wang, Kewei ; Liao, Wei-keng ; Choudhary, Alok ; Agrawal, Ankit ( December 2022 , 2022 International Conference on Computational Science and Computational Intelligence (CSCI))
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. Cyclic Shuffle-Compatibility Via Cyclic Shuffle Algebras

   https://doi.org/10.1007/s00026-023-00669-9  

   Liang, Jinting ; Sagan, Bruce E. ; Zhuang, Yan ( October 2023 , Annals of Combinatorics)

   A permutation statistic$${{\,\textrm{st}\,}}$$$\text{st}$is said to be shuffle-compatible if the distribution of$${{\,\textrm{st}\,}}$$$\text{st}$over the set of shuffles of two disjoint permutations$$\pi $$$\pi$and$$\sigma $$$\sigma$depends only on$${{\,\textrm{st}\,}}\pi $$$\text{st}\pi$,$${{\,\textrm{st}\,}}\sigma $$$\text{st}\sigma$, and the lengths of$$\pi $$$\pi$and$$\sigma $$$\sigma$. Shuffle-compatibility is implicit in Stanley’s early work onP-partitions, and was first explicitly studied by Gessel and Zhuang, who developed an algebraic framework for shuffle-compatibility centered around their notion of the shuffle algebra of a shuffle-compatible statistic. For a family of statistics called descent statistics, these shuffle algebras are isomorphic to quotients of the algebra of quasisymmetric functions. Recently, Domagalski, Liang, Minnich, Sagan, Schmidt, and Sietsema defined a version of shuffle-compatibility for statistics on cyclic permutations, and studied cyclic shuffle-compatibility through purely combinatorial means. In this paper, we define the cyclic shuffle algebra of a cyclic shuffle-compatible statistic, and develop an algebraic framework for cyclic shuffle-compatibility in which the role of quasisymmetric functions is replaced by the cyclic quasisymmetric functions recently introduced by Adin, Gessel, Reiner, and Roichman. We use our theory to provide explicit descriptions for the cyclic shuffle algebras of various cyclic permutation statistics, which in turn gives algebraic proofs for their cyclic shuffle-compatibility.

    

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4. A Shuffle Theorem for Paths Under Any Line

   https://doi.org/10.1017/fmp.2023.4  

   Blasiak, Jonah ; Haiman, Mark ; Morse, Jennifer ; Pun, Anna ; Seelinger, George H. ( January 2023 , Forum of Mathematics, Pi)

   Abstract We generalize the shuffle theorem and its $(km,kn)$ version, as conjectured by Haglund et al. and Bergeron et al. and proven by Carlsson and Mellit, and Mellit, respectively. In our version the $(km,kn)$ Dyck paths on the combinatorial side are replaced by lattice paths lying under a line segment whose x and y intercepts need not be integers, and the algebraic side is given either by a Schiffmann algebra operator formula or an equivalent explicit raising operator formula. We derive our combinatorial identity as the polynomial truncation of an identity of infinite series of $\operatorname {\mathrm {GL}}_{l}$ characters, expressed in terms of infinite series versions of LLT polynomials. The series identity in question follows from a Cauchy identity for nonsymmetric Hall–Littlewood polynomials. 

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5. A half-shear-half-shuffle mechanism and the single-layer twinning dislocation for {112¯2}〈112¯3¯〉 mode in hexagonal close-packed titanium

   https://doi.org/10.1016/j.actamat.2021.117150  

   Li, Jingwei ; Sui, Manling ; Li, Bin ( September 2021 , Acta Materialia)

   null (Ed.)