The Quot scheme of points $\mathrm {Quot} _ {d, n}(X) $ on a variety $ X $ over a field $ k $
parametrizes quotient sheaves of $\mathcal {O} _X^{\oplus d} $ of zero-dimensional support …

We consider two motivic generating functions defined on a variety, and reveal their tight
connection. They essentially count torsion-free bundles and zero-dimensional sheaves. On …

We define monotone links on a torus, obtained as projections of curves in the plane whose
coordinates are monotone increasing. Using the work of Morton-Samuelson, to each …

We introduce a family of generalized Schr\" oder polynomials $ S_\tau (q, t, a) $, indexed by
triangular partitions $\tau $ and prove that $ S_\tau (q, t, a) $ agrees with the Poincar\'e …

We define generalized Schröder polynomials Sλ (q, t, a) for triangular partitions and prove
that these polynomials recover the triangular (q, t)-Catalan polynomials of [2] at a= 0 …