Tongming Niu

collaborators

15 papers

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 $I^´_{r} (n)$ for the minimum, over all $r$ -colourings $I ¨ : (3 [ n ]) \to [r]$ , of $\max_{\mathcal{S}} \mathr…

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 $I^_{n}$ is the subgraph of the hypercube $Q_{n}$ induced by binary strings with no two consecutive ones. We determine $I ¨ (I^_{n}) = 2^{n}$ for $n \leq 6$ , so the…

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…

math.CO2026

A short proof of Mathar's 2013 recurrence conjecture for the reversible-binary-string sequence A032123

Tong Niu

For the OEIS sequence A032123, the number of length- $2 n$ black-and-white strings with $n$ black beads, considered up to reversal, R. J. Mathar contributed in November 2013 the conj…

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

A short proof of Mathar's 2013 recurrence conjecture for the reversible-binary-string sequence A032123

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