Shisheng Li

collaborators

7 papers

math.NT2026

Coprime pairs with equal sum of divisors, assuming smooth shifted primes

Shisheng Li, Zhong Zhuang

Let $h (x)$ be the number of pairs $1 \leq a < b < x$ with $g cd (a, b) = 1$ and $σ (a) = σ (b)$ . Erdős Problem #824 asks whether $h (x) > x^{2 - o (1)}$ . By an argument of Pollack and Pomerance, this…

math.NT2026

Unit fractions with semiprime denominators: an elementary proof of Erdős Problem #306

Shisheng Li

We give an elementary proof that every positive rational number $a / b$ with $b$ squarefree is a finite sum of distinct unit fractions $1/ n$ , where each $n$ is a product of two disti…

math.CO2026

Asymptotics of the Tchoukaillon array and a conjecture of Beluhov

Shisheng Li

The Tchoukaillon array is an infinite array of the positive integers, arising from a one-row Mancala solitaire, in which each positive integer occurs exactly once. Its zeroth colum…

math.NT2026

Every natural number is a sum of distinct semiprime unit fractions

Shisheng Li

We prove that every natural number is a finite sum of distinct unit fractions whose denominators are semiprimes (products of two distinct primes). This is the $ω = 2$ integer case of…

math.CO2026

Nonexistence of Whirling-Knight Tours at Half Coil Count for $n \equiv 4, 6 (mod 8)$

Shisheng Li

A whirling knight's tour is a Hamiltonian cycle in the digraph of counter-clockwise knight steps about the centre of an $n \times n$ board; its coil count $c$ is the winding number…

math.CO2026

$SB (3, n)$ has no Hamiltonian cycle when $n$ is even: a sign-of-permutation proof, with extension to all odd $m \equiv 3 (mod 4)$

Shisheng Li

We resolve exercise 7.2.2.4--224 of Knuth's Pre-Fascicle 8a (10 April 2026 draft, rated [46]): the digraph $SB (3, n)$ has no Hamiltonian cycle when $n$ is even. The argumen…

cs.DS2026

A note on the parameter $ℓ$ in Buchbinder--Feldman's deterministic submodular matroid algorithm

Shisheng Li

Buchbinder and Feldman recently gave a deterministic $(1 - 1/ e - ε)$ -approximation for maximizing a non-negative monotone submodular function subject to a matroid constraint,…

Coprime pairs with equal sum of divisors, assuming smooth shifted primes

Unit fractions with semiprime denominators: an elementary proof of Erdős Problem #306

Asymptotics of the Tchoukaillon array and a conjecture of Beluhov

Every natural number is a sum of distinct semiprime unit fractions

Nonexistence of Whirling-Knight Tours at Half Coil Count for n≡4,6(mod8)

SB(3,n) has no Hamiltonian cycle when n is even: a sign-of-permutation proof, with extension to all odd m≡3(mod4)

A note on the parameter ℓ in Buchbinder--Feldman's deterministic submodular matroid algorithm

Nonexistence of Whirling-Knight Tours at Half Coil Count for $n \equiv 4, 6 (mod 8)$

$SB (3, n)$ has no Hamiltonian cycle when $n$ is even: a sign-of-permutation proof, with extension to all odd $m \equiv 3 (mod 4)$

A note on the parameter $ℓ$ in Buchbinder--Feldman's deterministic submodular matroid algorithm