A binomial coefficient identity associated with Beukers' conjecture on Apéry numbers.
A binomial representation of the 3x + 1 problem
A card shuffling analysis of deformations of the Plancherel measure of the symmetric group.
A CAT algorithm for the exhaustive generation of ice piles
We present a CAT (constant amortized time) algorithm for generating those partitions of n that are in the ice pile model(n), a generalization of the sand pile model(n). More precisely, for any fixed integer k, we show that the negative lexicographic ordering naturally identifies a tree structure on the lattice (n): this lets us design an algorithm which generates all the ice piles of (n) in amortized time O(1) and in space O().
A CAT algorithm for the exhaustive generation of ice piles
We present a CAT (constant amortized time) algorithm for generating those partitions of n that are in the ice pile model(n), a generalization of the sand pile model(n). More precisely, for any fixed integer k, we show that the negative lexicographic ordering naturally identifies a tree structure on the lattice (n): this lets us design an algorithm which generates all the ice piles of (n) in amortized time O(1) and in space O().
A Catalan transform and related transformations on integer sequences.
A census of vertices by generations in regular tessellations of the plane.
A chaotic cousin of Conway's recursive sequence.
A characterization for all interval doubling schemes of the lattice of permutations.
A characterization of determinacy for Turing degree games
A Characterization of Multidimensional -Automatic Sequences
An infinite word is -automatic if, for all , its st letter is the output of a deterministic automaton fed with the representation of in the considered numeration system . In this extended abstract, we consider an analogous definition in a multidimensional setting and present the connection to the shape-symmetric infinite words introduced by Arnaud Maes. More precisely, for , we state that a multidimensional infinite word over a finite alphabet is -automatic for some abstract numeration...
A characterization of the simplex.
A closed formula for the number of convex permutominoes.
A closer look at lattice points in rational simplices.
A closer look at some new identities.
A colorful involution for the generating function for signed Stirling numbers of the first kind.
A combinatorial approach to hyperharmonic numbers.
A combinatorial approach to partitions with parts in the gaps
Many links exist between ordinary partitions and partitions with parts in the “gaps”. In this paper, we explore combinatorial explanations for some of these links, along with some natural generalizations. In particular, if we let be the number of partitions of n into j parts where each part is ≡ k (mod m), 1 ≤ k ≤ m, and we let be the number of partitions of n into j parts where each part is ≡ k (mod m) with parts of size k in the gaps, then .
A combinatorial derivation of the number of labeled forests.
A combinatorial derivation of the PASEP stationary state.