Tong-Ming Niu

collaborators

16 papers

cs.DC2026

Toward a Formally Verified Optimality Certificate for OGR(29): A SAT-Encoding Methods Note with Small-Case Demos

Tong Niu

A Golomb ruler of order~ $n$ is an integer set ${a_{0} < a_{1} < \dots < a_{n - 1}}$ whose $(2 n)$ pairwise differences $a_{j} - a_{i}$ ( $i < j$ ) are all distinct. The optimal Golomb ruler pr…

math.CO2026

An exact small- $n$ computation of the minimum 2-coloring discrepancy of $K_{n}^{(3)}$

Tong Niu

For an integer $r \geq 2$ and an order $n \equiv 1, 3 (mod 6)$ , write $δ_{r} (n)$ for the minimum, over all $r$ -colourings $χ : (3 [ n ]) \to [r]$ , of $\max_{\mathcal{S}} \mathrm{…

math.NT2026

Parity vectors and paradoxical sequences in the accelerated Collatz map

Tong Niu

This note studies parity vectors and paradoxical sequences in the accelerated Collatz iteration $T (n) = (3 n + 1) /2$ for $n$ odd, $T (n) = n /2$ for $n$ even. Building on Rozier and Ter…

math.CO2026

The pebbling number of Fibonacci cubes

Tong Niu

The $n$ -th Fibonacci cube $Γ_{n}$ is the subgraph of the hypercube $Q_{n}$ induced by binary strings with no two consecutive ones. We determine $π (Γ_{n}) = 2^{n}$ for $n \leq 6$ , so the peb…

math.CO2026

An explicit algebraic generating function for OEIS A348410

Tong Niu

For the OEIS sequence A348410, P. Bala recorded in February 2022 two equivalent closed forms, $a (n) = [x^{n}] ((1 - x) (1 - x^{2}))^{- n}$ and a single-index binomial sum. R. J. Mathar (Oc…

math.CO2026

Three short proofs of Mathar's 2014 conjecture for OEIS A002627

Tong Niu

For the OEIS sequence A002627, defined by the inhomogeneous first-order recurrence $a (n) = n a (n - 1) + 1$ with $a (0) = 0$ , R.~J.~Mathar recorded in February 2014 the conjectured se…

Toward a Formally Verified Optimality Certificate for OGR(29): A SAT-Encoding Methods Note with Small-Case Demos

An exact small-n computation of the minimum 2-coloring discrepancy of Kn(3)​

Parity vectors and paradoxical sequences in the accelerated Collatz map

The pebbling number of Fibonacci cubes

An explicit algebraic generating function for OEIS A348410

Three short proofs of Mathar's 2014 conjecture for OEIS A002627

An exact small- $n$ computation of the minimum 2-coloring discrepancy of $K_{n}^{(3)}$