A 2-coloring of can have monochromatic Schur triples, but not less.
-analogue of some binomial coefficient identities of Y. Sun.
A bijection between 3-Motzkin paths and Schröder paths with no peak at odd.
A bijection between atomic partitions and unsplitable partitions.
A bijection between classes of fully packed loops and plane partitions.
A bijection between planar constellations and some colored Lagrangian trees.
A bijection on Dyck paths and its cycle structure.
A bijective proof of a major index theorem of Garsia and Gessel.
A bijective proof of Borchardt's identity.
A bijective proof of Garsia's -Lagrange inversion theorem.
A bijective proof of the hook-content formula for super Schur functions and a modified jeu de taquin.
A binomial coefficient identity associated to a conjecture of Beukers.
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.