Ken Ono

collaborators

24 papers

math.NT2026

Ternary polynomial relations and periods of cusp forms

Vasily Ilin, Ken Ono

Bachmann and van Ittersum conjectured that every polynomial $f \in Q [x, y, z]$ satisfying $f (x, y, z) = f (y, z, x), f (x, y, z) + f (- y, x - y, z) + f (y - x, - x, z) = 0$ is a sum of polynom…

math.NT2026

Rogers--Ramanujan identities from the geometry of $X^{a} = Y^{b}$

Yifeng Huang, Kenny Lau, Ken Ono

We prove the conjecture of Huang, Jiang, and Oblomkov (HJO) giving a geometric extension of the Rogers--Ramanujan and Andrews--Gordon identities for every torus-knot singularity $X…

math.CO2026

Zero-free columns in character tables of symmetric groups

Colin Defant, Sidharth Hariharan, Kenny Lau +1

The rows and columns of the character table of the symmetric group $S_{n}$ are both naturally indexed by partitions of $n$ . Let $D (n)$ denote the number of conjugacy classes of $S_{n}$ …

math.PR2026

Proof of the Lyons--White Conjecture

Colin Defant, Ken Ono

Let $D_{n}$ be the dihedral group of order $2 n$ . Consider a continuous-time random walk on $D_{n}$ driven by arbitrary symmetric rates whose support generates $D_{n}$ . For $p\in[1,\infty…

math.NT2026

Algebraic geometric framework of Rogers--Ramanujan identities

Yifeng Huang, Kenny Lau, Ken Ono +1

The Rogers--Ramanujan identities equate a $q$ -series whose exponents are governed by a quadratic form with an infinite product supported on two residue classes modulo~ $5$ . Identiti…

math.NT2026

Formalized $q$ -series: The Rogers-Ramanujan Identities and Beyond

Kenny Lau, Seewoo Lee, Ken Ono

The theory of $q$ -series and basic hypergeometric series plays a crucial role at the intersection of combinatorics, number theory, and representation theory. From the classical par…

math.NT2026

Modularity of Point Counts for the Curves $X^{a} = Y^{b}$ : New Rogers--Ramanujan Identities

Kenny Lau, Ken Ono

For coprime $1 < a < b$ , let $M_{n}^{a, b} (F_{q})$ be the set of commuting pairs of nilpotent $n \times n$ matrices over $F_{q}$ with $X^{a} = Y^{b}$ . Huang, Jiang, and Oblomkov as…

math.CO2026

A bijective proof of a partition theorem of Berkovich and Uncu

Michal Mogielnicki, Ken Ono, Niels Voss +1

In 2016, Berkovich and Uncu proved that, for all nonnegative integers $i$ , $j$ , and $n$ , the number of strict partitions of $n$ with $i$ odd-indexed odd parts and $j$ even-indexed…

math.CO2026

On a conjecture of Han and Xiong for fractional Gaussian binomial coefficients

Ken Ono

Han and Xiong recently extended the Gaussian binomial coefficient $[k r + k]_{q}$ to positive rational $r$ and conjectured that its integer trace, the integer-e…

math.NT2026

Beyond Mock Modularity: Elliptic Corrections for Higher Dyson Ranks

Claudia Alfes, Ken Ono, Ashvin Swaminathan

When $m = 1$ , the Dyson rank generating function is a classical bridge between partition theory, Ramanujan's mock theta functions, and the theory of harmonic Maass forms and nonhol…

math.CO2026

Record compositions of alternating permutations and noncommutative symmetric functions

Evan Chen, Ken Ono, Michal Mogielnicki

Amdeberhan, Shareshian, and Stanley recently proved that a function $φ$ arising in the theory of partition Eisenstein series counts the alternating permutations of ${1, \dots, 2 n}$ …

math.NT2026

Integer values of $tan (arctan 1 + arctan 2 + \dots + arctan n)$ are rare

Ken Ono

For $n \geq 1$ , we let $x_{n} := tan (k = 1 \sum n arctan k) .$ In 2008, Amdeberhan, Medina, and Moll conjectured that $x_{n} \neq \in Z$ for every $n \geq 5$ . This was kn…

math.NT2026

Thakur's hypotheses on power sums of $F_{q} [t]$

Evan Chen, Ken Ono

In his 2009 paper, Thakur posed three conjectural hypotheses for the degrees of the power sums \[ S_d(k)=\sum_{\substack{a\in \mathbb F_q[t] \text{ monic}\\ °a=d}} a^{-k} \qquad\te…

math.CO2026

A problem of Andrews and Dhar on partitions

Simon Mahns, Ken Ono, Jujian Zhang

This paper is motivated by a broad question about AI-assisted mathematics: can an AI system help discover and certify an explicit bijection between two infinite sequences of compli…

math.NT2026

Four-digit Kaprekar dynamics in odd bases

Evan Chen, Ken Ono, Richard E. Schwartz +1

Start with four digits, arrange them in both descending and ascending order, subtract, and repeat. This simple process is known as the Kaprekar routine, famous in base ten for send…

math.CO2026

Reciprocals of Partition Polynomials

Evan Chen, Ken Ono, Jujian Zhang

Ballantine--Beck--Feigon--Maurischat introduced the subsum polynomial \[ \operatorname{sp}(λ,x):=\prod_i (1+x^{λ_i}) \] attached to an integer partition $λ$ , and studied rational f…

math.RT2026

Chebyshev quotients, Demazure multiplicities, and Dyck-path models

Rekha Biswal, Ken Ono, Jujian Zhang

We study Chebyshev quotients that arise in the representation theory of Lie algebras, specifically within the theory of Demazure flags for fusion products of $sl_{2} [t]$ -m…

math.NT2026

ABC implies that Ramanujan's tau function misses almost all primes

David Kurniadi Angdinata, Evan Chen, Chris Cummins +21

Lehmer conjectured that Ramanujan's tau-function never vanishes. In a related direction, a folklore conjecture asserts that infinitely many primes arise as absolute values of Raman…

math.DS2026

On the paucity of lattice triangles

David Kurniadi Angdinata, Evan Chen, Ken Ono +3

A rational triangle $T$ (one whose angles are rational multiples of $π$ ) unfolds to a translation surface $X_{T}$ . The lattice triangle problem asks to classify those $T$ for which…

math.CO2026

Dead ends in square-free digit walks

Evan Chen, Chris Cummins, Ben Eltschig +18

We study "dead ends" in square-free digit walks: square-free integers $N$ such that, in base $b$ , every one-digit extension $b N + d$ is non-square-free. In base $10$ , the stochastic…

math.NT2026

Almost all primes are partially regular

Evan Chen, Chris Cummins, Ben Eltschig +18

For odd primes $p$ , we let $K_{p} := Q (ζ_{p})$ be the $p$ th cyclotomic field and let $ω$ denote its Teichmuller character. For $α > 1/2$ , we say that an odd prime $p$ is partially…

math.NT2026

Parity of $k$ -differentials in genus zero and one

Dawei Chen, Evan Chen, Kenny Lau +2

Here we completely determine the spin parity of $k$ -differentials with prescribed zero and pole orders on Riemann surfaces of genus zero and one. This result was previously obtaine…

math.CO2026

Fel's Conjecture on Syzygies of Numerical Semigroups

Evan Chen, Chris Cummins, GSM +18

Let $S = ⟨ d_{1}, \dots, d_{m} ⟩$ be a numerical semigroup and $k [S]$ its semigroup ring. The Hilbert numerator of $k [S]$ determines normalized alternating syzygy power sums $K_…

math.NT2025

Parity of the partition function in quadratic progressions

Ken Ono, Ashvin Swaminathan

The parity of the partition function $p (n)$ is one of the most stubborn problems in number theory. In 2010, the first author conjectured, for square-free $1 < D \equiv 23 (mod 24)$ , t…

Ternary polynomial relations and periods of cusp forms

Rogers--Ramanujan identities from the geometry of Xa=Yb

Zero-free columns in character tables of symmetric groups

Proof of the Lyons--White Conjecture

Algebraic geometric framework of Rogers--Ramanujan identities

Formalized q-series: The Rogers-Ramanujan Identities and Beyond

Modularity of Point Counts for the Curves Xa=Yb: New Rogers--Ramanujan Identities

A bijective proof of a partition theorem of Berkovich and Uncu

On a conjecture of Han and Xiong for fractional Gaussian binomial coefficients

Beyond Mock Modularity: Elliptic Corrections for Higher Dyson Ranks

Record compositions of alternating permutations and noncommutative symmetric functions

Integer values of tan(arctan1+arctan2+⋯+arctann) are rare

Thakur's hypotheses on power sums of Fq​[t]

A problem of Andrews and Dhar on partitions

Four-digit Kaprekar dynamics in odd bases

Reciprocals of Partition Polynomials

Chebyshev quotients, Demazure multiplicities, and Dyck-path models

ABC implies that Ramanujan's tau function misses almost all primes

On the paucity of lattice triangles

Dead ends in square-free digit walks

Almost all primes are partially regular

Parity of k-differentials in genus zero and one

Fel's Conjecture on Syzygies of Numerical Semigroups

Parity of the partition function in quadratic progressions

Rogers--Ramanujan identities from the geometry of $X^{a} = Y^{b}$

Formalized $q$ -series: The Rogers-Ramanujan Identities and Beyond

Modularity of Point Counts for the Curves $X^{a} = Y^{b}$ : New Rogers--Ramanujan Identities

Integer values of $tan (arctan 1 + arctan 2 + \dots + arctan n)$ are rare

Thakur's hypotheses on power sums of $F_{q} [t]$

Parity of $k$ -differentials in genus zero and one