Combinatorics

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Contents

• Boundary Arithmetic-Progression Intersection Bound
• Arithmetic Progressions and Boundary Codes
• AbelianBorders
• Apwenian
• Cyclic Pattern Avoidance
• Padovan Enumeration of Cyclic Avoiders
• Uniqueness of the Padovan Subsequence
• Insertion Branches for Padovan Words
• Separated Permutation Blocks
• Rooted Cycle-Word Classes
• Padovan Counting Recurrence
• Recovering a Cyclic Permutation
• Decomposing Padovan Cycle Words
• Pattern Occurrences in Padovan Words
• Rotations and Circular Subwords
• Successors of Padovan Cycle Words
• Triples in Separated Blocks
• Tetranacci Enumeration of Cyclic Avoiders
• From Cycle Words to Permutations
• Four-Branch Decomposition
• Low-Arc Insertion
• One-Line Avoidance Under Insertion
• Pattern Constraints on Cycle Arcs
• Structure of Admissible Cycle Words
• Successors After Low-Arc Insertion
• Enumeration of (32; 1 to 3) Avoiders
• From the Recurrence to the Cubic
• Reconstructing the Final Cycle
• Value Gaps and Closed Edges
• Catalan Orders of the Final Cycle
• Splitting at the Largest Value
• The (32; 1 to 3) Avoidance Series
• Encoding the Value Gaps
• The Final-Cycle Bijection
• Refined Counts by Final Cycle
• Uniqueness of the Distinguished Series
• Fixed Points and the Two Avoidance Conditions
• Counting Words by Their Fixed Points
• Arrow Patterns and Their Avoidance Classes
• The Arrow-Wilf Equivalence
• Insertion and Singleton Cycles
• Gap Vectors and Interleaved Words
• Partitions by Extremal Fixed Points
• Finite Sums for the Arrow-Wilf Equivalence
• Counting the First Decorated Family
• Decorated Objects for the First Pattern
• Counting the First Arrow-Pattern Avoiders
• Uniqueness of the First Decorated Description
• Recovering First-Pattern Decorated Data
• Decorated Objects for the Second Pattern
• Counting the Second Arrow-Pattern Avoiders
• Inverting the Second Decorated Construction
• Balanced Compositions Are Counted by Nonnegative Walks from Height Two
• BinomialBases
• Cardinality-Sum-Avoiding Subsets
• CatalanPowerHankel
• A Two-Term Refutation of the Gijswijt Merge Identity
• CircularWords
• CrosswordGrid
• A Permutation Grid with 155 Rook Placements
• Every Natural Rook-Placement Count Occurs
• Crossword Grids and Rook Placements
• Cyclic Latin Eulerian Numbers Are Not Fully Symmetric
• CylindricPartition
• Richman’s congruence for A053871
• DigitHankel
• DottedStack
• Factoring the Cycles of the Modular Multiplicative Ducci Game
• DyckValleys
• The Conjectured Classification of Erdos-Deep Triples Is Incomplete
• The Erdos-Graham Order Gadget Is Impossible at Every Scale
• Asymptotics of the Optimal Fair-Window Defect
• A Lower Bound for Deterministic Fair-Input Window Rules
• Deterministic Word-Minimum Window Tables
• A Finite Upper Bound for Fair-Source Window Defects
• Fishburn
• FishburnTenSeven
• FishburnTenThirteen
• FundamentalBijection
• GeneralizedPetersen
• Geometry
• A Colored-Path Determinant Counterexample
• Graph
• GreedyBrick
• GroupActions
• GroupWords
• Hamming
• Hypermatrix
• IndecomposableInversion
• InversionSeq
• The smallest set of uniqueness for the Ising cone
• Kimberling’s least-two-element subset count
• The Knight-Dialler Recurrence
• Latin
• Row Counting and Row Reversal
• Latin Squares and Column Ascents
• The Shifted-Square Ascent Formula
• Interior Multiples of the Latin Eulerian Total
• Explicit Permutation Statistics
• Residue Comparisons After Swapping Zero and One
• Mathar’s recurrence for A068551
• Walks of near-maximal algebraic area on the square lattice
• Zero Slope Is Optimal Exactly When the Weighted Index Sum Is Balanced
• LevelSequence
• MeshPattern
• MetallicHankel
• MotzkinHankel
• NarayanaStrip
• Nonnesting
• OddIndependence
• Eventual periodicity of the self-banning rows
• Orthogonality
• PackingDomatic
• Pan-Skandera-Wang Bruhat Theorem
• Pan-Skandera-Wang Bruhat Definitions
• Pan-Skandera-Wang Selection Invariant
• An Alternating Stirling Identity for Fibonacci and Lucas Numbers
• Parking
• PartialTheta
• Reversal and the Weighted Sum of a Partition
• Partitions
• PatternMatchings
• PerfectMatchings
• Permanental
• Permutation
• PermutationArrays
• PermutationSquare
• Polyomino
• PopStack
• PrefixCovers
• Probability
• QGrammar
• Quasi-Injectivity Is Not Closed Under Composition
• Separating the Orders of Quasi-Injectivity
• RegularInduced
• RestrictedSchur
• RotationAvoidance
• Scarf
• SemiMeanderSecondDiagonal
• The Second Semi-Meander Diagonal
• Conjecture 15 of CayleyPy-4 fails at k = 5, L = 4, N = 13
• Conjecture 16 of CayleyPy-4 fails at k = 4, L = 2, N = 5
• Diameter of the inverse-closed consecutive 3-cycle Schreier coset graph
• Partitions with the fewest extensions are boxes
• Splines
• Squarefree Numbers Have No Partition Whose Parts and Multiplicities Agree in Mean
• The Unlucky-Car Spectrum of Stirling Permutations
• SubspaceCodes
• TwoColorPartition
• Two-layer solid partitions with a second layer of size 3
• VincularStack
• WeakAscent
• The extinction set of the wheel W_18 contains 4
• XorTriangle
• Mathar’s recurrence for A108958
• Zigzag