4 papers
Bounding and Approximating Kostka Numbers
Jonathan Leake, Zirou Zhang
Kostka numbers, the coefficients of Schur polynomials, count semistandard Young tableaux of prescribed shape and weight. We give a deterministic algorithm for approximating Kostka…
Log-concavity and Approximate Counting for Totally Unimodular Polytopes
Jonathan Leake, Maryam Mohammadi Yekta
We present a new lower bound on the number of lattice points of all totally unimodular polytopes, generalizing previous lower bounds on contingency tables, integer flows, and beyon…
New Bounds for Integer Flows and Verma Modules, via Denormalized Lorentzian Laurent Series
Jonathan Leake, Maryam Mohammadi Yekta
The theory of log concave polynomials has recently been developed to study objects and problems in combinatorics and other subfields in mathematics. Particular classes of log conca…
Capacity bounds on integral flows and the Kostant partition function
Jonathan Leake, Alejandro H. Morales
The type Kostant partition function is an important combinatorial object with various applications: it counts integer flows on the complete directed graph, computes Hilbert ser…