Related papers: Counting with rational generating functions
We study algebraic algorithms for expressing the number of non-negative integer solutions to a unimodular system of linear equations as a function of the right hand side. Our methods include Todd classes of toric varieties via Gr\"obner…
This paper introduces a more restrictive notion of feasibility of functionals on Baire space than the established one from second-order complexity theory. Thereby making it possible to consider functions on the natural numbers as running…
In binary polynomial optimization, the goal is to find a binary point maximizing a given polynomial function. In this paper, we propose a novel way of formulating this general optimization problem, which we call factorized binary polynomial…
A polynomial-time algorithm is produced which, given generators for a group of permutations on a finite set, returns a direct product decomposition of the group into directly indecomposable subgroups. The process uses bilinear maps and…
We find generating functions the number of strings (words) containing a specified number of occurrences of certain types of order-isomorphic classes of substrings called subword patterns. In particular, we find generating functions for the…
We present an elementary method for proving enumeration formulas which are polynomials in certain parameters if others are fixed and factorize into distinct linear factors over Z. Roughly speaking the idea is to prove such formulas by…
We study Boolean functions of an arbitrary number of input variables that can be realized by simple iterative constructions based on constant-size primitives. This restricted type of construction needs little global coordination or control…
We give a technical overview of our exact-real implementation of various representations of the space of continuous unary real functions over the unit domain and a family of associated (partial) operations, including integration, range…
In this paper we use computational method based on operational point of view to prove a new generating function of exponential polynomials. We give its applications involving geometric polynomials, Bernoulli and Euler numbers.
Kawamura and Cook specified the least set of information about a continuous function on the unit interval which is needed for fast function evaluation. This paper presents a variation of their result. To make the above statement precise,…
We give two natural definitions of polynomial-time computability for L2 functions; and we show them incomparable (unless complexity class FP_1 includes #P_1).
We consider the following problem: Given a rational matrix $A \in \setQ^{m \times n}$ and a rational polyhedron $Q \subseteq\setR^{m+p}$, decide if for all vectors $b \in \setR^m$, for which there exists an integral $z \in \setZ^p$ such…
We consider stochastic and open quantum systems with a finite number of states, where a stochastic transition between two specific states is monitored by a detector. The long-time counting statistics of the observed realizations of the…
Let $k$ be a finite field extension of the function field $\bfF_p(T)$ and $\bar{k}$ its algebraic closure. We count points in projective space $\Bbb P ^{n-1}(\bar{k})$ with given height and of fixed degree $d$ over the field $k$. If…
A common theme of enumerative combinatorics is formed by counting functions that are polynomials evaluated at positive integers. In this expository paper, we focus on four families of such counting functions connected to hyperplane…
In this paper we develop a functional calculus for a countable system of generators of contraction strongly continuous semigroups. As a symbol class of such calculus we use the algebra of polynomial tempered distributions. We prove a…
Endowing the set of functional graphs (FGs) with the sum (disjoint union of graphs) and product (standard direct product on graphs) operations induces on FGs a structure of a commutative semiring R. The operations on R can be naturally…
A solution is proposed for the problem of composition of ordinary generating functions. A new class of functions that provides a composition of ordinary generating functions is introduced; main theorems are presented; compositae are written…
Two emergent properties in aggregation theory are investigated, namely horizontal maxitivity and comonotonic maxitivity (as well as their dual counterparts) which are commonly defined by means of certain functional equations. We completely…
Krawtchouk polynomials appear in a variety of contexts, most notably as orthogonal polynomials and in coding theory via the Krawtchouk transform. We present an operator calculus formulation of the Krawtchouk transform that is suitable for…