11 papers
Record compositions of alternating permutations and noncommutative symmetric functions
Evan Chen, Ken Ono, Michal Mogielnicki
The paper determines the exact count of alternating permutations of even length with a given record composition, expressing the numbers using binomial coefficients and Euler number…
Parity of -differentials in genus zero and one
Dawei Chen, Evan Chen, Kenny Lau +2
Here we completely determine the spin parity of -differentials with prescribed zero and pole orders on Riemann surfaces of genus zero and one. This result was previously obtaine…
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…
Thakur's hypotheses on power sums of
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\t…
Fel's Conjecture on Syzygies of Numerical Semigroups
Evan Chen, Chris Cummins, GSM +18
Let be a numerical semigroup and its semigroup ring. The Hilbert numerator of determines normalized alternating syzygy power sums $K_…
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 , and studied rationa…