3 papers
math.CO2026
Cyclotomic generating functions, empty weighted complete intersections and positivity
Mona Gatzweiler, Fabián Levicán-Santibáñez, Atsuro Yoshida
We give a sufficient combinatorial condition for the non-negativity of the coefficients of polynomial quotients of products of -integers, also known as cyclotomic generating fun…
math.CO2026
More minor summation formulae
Shane Chern, Theresia Eisenkölbl, Ilse Fischer +8
We prove determinantal-Pfaffian formulae that simultaneously generalise the Pfaffian minor summation formula of Ishikawa and Wakayama and Byun's recent minor summation formula. The…
math.CO2025
A positivity conjecture for a quotient of -binomial coefficients
Mona Gatzweiler, Christian Krattenthaler
We conjecture that, if the quotient of two -binomial coefficients with the same top argument is a polynomial, then it has non-negative coefficients. We summarise what is known a…