Tong-Ming Niu

collaborators

18 papers

math.CO2026

Non-adjacent triples of cells in a triangular grid: proofs of three conjectured generating functions

Tong Niu

Let $\Tn$ be the triangular grid of side $n$ , with its $n^{2}$ unit cells, and let two cells be side-adjacent if they share an edge and point-adjacent if they share a vertex. We coun…

math.CO2026

The first descent in a standard Young tableau of shape $(n, n, n)$

Tong Niu

Let $a (n)$ be the number of standard Young tableaux of shape $(n, n, n)$ whose entry in row $2$ , column $1$ is odd; equivalently, the number of those whose first descent is even. Thi…

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…

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…

math.CO2026

Improved Upper Bounds on the Pebbling Numbers of the Blanuša Snarks

Tong Niu

The two Blanuša snarks $B_{1}$ and $B_{2}$ are 3-regular graphs on 18 vertices. Dantas, Lordelo, Niedermaier and Nogueira (Discrete Appl. Math. 361, 2025, pp. 336-346) established the…

math.CO2026

Graceful labelings of spiders with three-edge legs and pendant leaves at the center

Tong Niu

A graph $G$ on $m$ edges is graceful if there is an injection $f : V (G) \to {0, 1, \dots, m}$ whose induced edge labels ${∣ f (u) - f (v) ∣ : uv \in E (G)}$ are exactly $\{1, 2, \l…

math.CO2026

Size-4 Counterexamples to the Sidon-Extension Conjecture

Tong Niu

A finite set $S \subset Z$ is a Sidon set if its pairwise differences are distinct. Recall that a perfect difference set (PDS) of order $n$ is a set $B \subset \mathbb{Z}_…

math.CO2026

A short proof of Mathar's 2021 recurrence conjecture for the Lehmer-Comtet diagonal A045406

Tong Niu

For OEIS sequence A045406, the column-2 diagonal of the Lehmer-Comtet triangle A008296, R. J. Mathar contributed in September 2021 the conjectured order-2 P-recursive recurrence \[…

math.CO2026

A short proof of Mathar's 2020 recurrence conjecture for the generalized-Stirling sequence A001711

Tong Niu

For the OEIS sequence A001711, contributed by N. J. A. Sloane long before the on-line era and identified there as the diagonal $T (n + 4, 4)$ of a generalized-Stirling triangle, R. J.…

math.CO2026

The vertex Folkman number $F_{v} (3, 3; 5)$ equals~ $8$

Tong Niu

The vertex Folkman number $F_{v} (s, t; k)$ is the smallest $n$ for which there exists a $K_{k}$ -free graph on $n$ vertices whose vertices cannot be $2$ -colored without producing a monoch…

math.CO2026

A short proof of Mathar's 2013 recurrence conjecture for the Laguerre sequence~A025166

Tong Niu

For the OEIS sequence A025166, defined by $a (n) = - n! 2^{n} L_{n} (1/2)$ where $L_{n}$ is the Laguerre polynomial of degree $n$ , R.~J.~Mathar contributed in February 2013 the conj…

math.CO2026

A short proof of Mathar's 2016 recurrence conjecture for OEIS A176677

Tong Niu

For the OEIS sequence A176677, defined by the quadratic convolution recurrence $a (0) = a (1) = 1$ and $a (n + 1) = \sum_{p = 0}^{n} a (p) a (n - p) - 1$ for $n \geq 1$ , R.~J.~Mathar contributed…

math.CO2026

A short proof of Mathar's 2013 recurrence conjecture for the Meixner sequence A214615

Tong Niu

For the OEIS sequence A214615, defined by $a (n) = M_{n} (1)$ where $M_{n}$ is the $n$ -th Meixner polynomial satisfying $M_{n + 1} (x) = x M_{n} (x) - n^{2} M_{n - 1} (x)$ , R.~J.~Mathar c…

Non-adjacent triples of cells in a triangular grid: proofs of three conjectured generating functions

The first descent in a standard Young tableau of shape (n,n,n)

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

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

Improved Upper Bounds on the Pebbling Numbers of the Blanuša Snarks

Graceful labelings of spiders with three-edge legs and pendant leaves at the center

Size-4 Counterexamples to the Sidon-Extension Conjecture

A short proof of Mathar's 2021 recurrence conjecture for the Lehmer-Comtet diagonal A045406

A short proof of Mathar's 2020 recurrence conjecture for the generalized-Stirling sequence A001711

The vertex Folkman number Fv​(3,3;5) equals~8

A short proof of Mathar's 2013 recurrence conjecture for the Laguerre sequence~A025166

A short proof of Mathar's 2016 recurrence conjecture for OEIS A176677

A short proof of Mathar's 2013 recurrence conjecture for the Meixner sequence A214615

The first descent in a standard Young tableau of shape $(n, n, n)$

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

The vertex Folkman number $F_{v} (3, 3; 5)$ equals~ $8$