Shisheng Li

collaborators

Showing math.COShow all

3 papers · 1 filter

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.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…

Asymptotics of the Tchoukaillon array and a conjecture of Beluhov

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)

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 $m \equiv 3 (mod 4)$