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Complement Submodular Information Measures for Balanced and Robust Data Selection A Proof of a Conjecture on Positive and Negative Square Energies of Unicyclic Graphs Laplacian Spectrum of the Weakly Zero-Divisor Graph of a Finite Commutative Ring An identity for second Eulerian numbers via lattice-point counting $t$-tone edge coloring of graphs Constructing Maximal Bumpless Pipedreams for Double Grothendieck Polynomials Mubayi's Polynomial-Ideal Conjecture and Cover-Ideal Turán Methods Implicit Binarization via Complex Phase Dynamics in Combinatorial Optimization The limits of Schur multipliers in Pólya conversion problems for the $q$-permanent function Universality theorems for generalized splines Framing Triangulations for Arbitrary Integer Flow Polytopes On the Common Generalization of Gentle Algebras and Framed Directed Acyclic Graphs The complexity of frugal digraph homomorphisms Chaotic and periodic behavior of jeu de taquin on infinite Young tableaux Enumerating Pattern Avoiding Parking Functions Incidence toric ideals and three-point functions Unique Winning Opening Move in Three-Row Chomp Strong majority colorings of graphs A Balancing Theorem for Spanning Trees of Rectangular Grid Graphs Spectral radius and edge-disjoint connected factors of graphs New invariants for rank metric codes, with applications to the classification of rank two semifields of order 256 Flexible DP-4-coloring of planar graphs without 4-cycles and intersecting triangles Balanced intersection size distributions in projective planes List Reconstruction Problem with List Size Two Is Dimensionality a Barrier for Retrieval Models? The INIEP: Irreducible and Positive Realizations The number of Pfaffian orientations on punctured polygonally cellulated surfaces Explicit Construction of Polytopes whose Ehrhart Polynomials Realize any Given Sign Pattern Finite-state enumeration of adjacency-constrained 132-avoiding permutations AMDS and quantum AMDS Constacyclic codes of length $4p^ς$ over $\mathbb{F}_{{p}^{m}}$
Exhaustive Generation of Pattern-Avoiding s-Words
Samuel Buick, Madeleine Goertz, Amos Lastmann, Kunal Pal, Helen · 2025-08-22 · via math.CO updates on arXiv.org

The most well-known Gray code of permutations is plain changes. It was discovered in the 1600s by bell-ringers who wished to order the permutations of [n] by swaps (e.g., 123, 132, 312, 321, 231, 213 for n = 3). In other words, plain changes traces a Hamilton path in the permutohedron. In 2013 it was shown that plain changes can be generated by a greedy algorithm: swap the largest value. Algorithm J replaces the swap operation with the jump operation (which moves a larger digit past one or more smaller digits) and forms the basis of the wildly successful Combinatorial Generation via Permutation Languages series of papers. Here we further generalize this line of research to languages of s-words (i.e., multiset permutations). We generalize jumps to bumps, which moves a sequential run of the same larger digit past one or more smaller digits. Algorithm B greedily applies minimum-length bumps prioritized by largest value, then largest index, then rightward before leftward (e.g. 1122, 1221, 1212, 2112, 2121, 2211 for s = (2, 2)). We show that the algorithm works for s-word languages avoiding a wide variety of tame patterns. Specific applications include efficient algorithm for generating s-Stirling words (which avoid 121) and new Gray codes for various s-Catalan objects (which avoid 132 and 121). The former result leads to Hamilton paths in every s-permutahedron.