-analogue of some binomial coefficient identities of Y. Sun.
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 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 characterization of determinacy for Turing degree games
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 proof of a partition identity of Andrews and Stanley.
A combinatorial proof of Andrews' smallest parts partition function.
A combinatorial proof of the sum of -cubes.
A complete categorization of when generalized Tribonacci sequences can be avoided by additive partitions.
A de Bruijn-type formula for enumerating patterns of partitions.
A discontinuity in the distribution of fixed point sums.
A fast algorithm for MacMahon's partition analysis.
A generalized formula of Hardy.
A left weighted Catalan extension.
A new class of infinite products, and Euler's totient.
A normalization formula for the Jack polynomials in superspace and an identity on partitions.
A note on representation functions with different weights
For any positive integer k and any set A of nonnegative integers, let denote the number of solutions (a₁,a₂) of the equation n = a₁ + ka₂ with a₁,a₂ ∈ A. Let k,l ≥ 2 be two distinct integers. We prove that there exists a set A ⊆ ℕ such that both and hold for all n ≥ n₀ if and only if log k/log l = a/b for some odd positive integers a,b, disproving a conjecture of Yang. We also show that for any set A ⊆ ℕ satisfying for all n ≥ n₀, we have as n → ∞.
A note on solid partitions