49 citations · 165 across the 22 of their papers we have counts for
17 papers · 1 filter
Counting with two-level polynomials
Tristram Bogart, Kevin Woods
We examine combinatorial counting functions with two parameters, and . For fixed , these functions are (quasi-)polynomial in . As varies, the degree of this polyno…
A Plethora of Polynomials: A Toolbox for Counting Problems
Tristram Bogart, Kevin Woods
A wide variety of problems in combinatorics and discrete optimization depend on counting the set of integer points in a polytope, or in some more general object constructed via…
The generalized Frobenius problem via restricted partition functions
Kevin Woods
Given relatively prime positive integers, , the Frobenius number is the largest integer with no representations of the form with nonnegative…
Periodic behavior in families of numerical and affine semigroups via parametric Presburger arithmetic
Tristram Bogart, John Goodrick, Kevin Woods
Let be polynomial functions of . For fixed , let be the numerical semigroup generated by $f_1(n),\ldots,f_k(n)…
A parametric version of LLL and some consequences: parametric shortest and closest vector problems
Tristram Bogart, John Goodrick, Kevin Woods
Given a parametric lattice with a basis given by polynomials in Z[t], we give an algorithm to construct an LLL-reduced basis whose elements are eventually quasi-polynomial in t: th…
Parametric Presburger arithmetic: logic, combinatorics, and quasi-polynomial behavior
Tristram Bogart, John Goodrick, Kevin Woods
Parametric Presburger arithmetic concerns families of sets S_t in Z^d, for t in N, that are defined using addition, inequalities, constants in Z, Boolean operations, multiplication…