Related papers: Enumeration formul{\ae} in neutral sets
Prefix normal words are binary words that have no factor with more $1$s than the prefix of the same length. Finite prefix normal words were introduced in [Fici and Lipt\'ak, DLT 2011]. In this paper, we study infinite prefix normal words…
We define an odometer in the Baire space. That is the non-compact space of one sided sequences of natural numbers. We go on to prove that it is topologically conjugated to the dyadic odometer restricted to an appropriate non-compact subset…
We study learning of indexed families from positive data where a learner can freely choose a hypothesis space (with uniformly decidable membership) comprising at least the languages to be learned. This abstracts a very universal learning…
We define a class of languages of infinite words over infinite alphabets, and the corresponding automata. The automata used for recognition are a generalisation of deterministic Muller automata to the setting of nominal sets. Remarkably,…
As a contribution to quantitative set-theoretic inferencing, a translation is proposed of conjunctions of literals of the forms $x=y\setminus z$, $x \neq y\setminus z$, and $z =\{x\}$, where $x,y,z$ stand for variables ranging over the von…
Narrowing extends term rewriting with the ability to search for solutions to equational problems. While first-order rewriting and narrowing are well studied, significant challenges arise in the presence of binders, freshness conditions and…
Set constraints provide a highly general way to formulate program analyses. However, solving arbitrary boolean combinations of set constraints is NEXPTIME-hard. Moreover, while theoretical algorithms to solve arbitrary set constraints…
Let A be a class of objects, equipped with an integer size such that for all n the number a(n) of objects of size n is finite. We are interested in the case where the generating fucntion sum_n a(n) t^n is rational, or more generally…
In studying the enumerative theory of super characters' of the group of upper triangular matrices over a finite field we found that the moments (mean, variance and higher moments) of novel statistics on set partitions have simple closed…
We introduce the notion of saturated sets of primes of an algebraic number field and prove an analogue of Riemann's existence theorem for the decomposition groups of infinite stably saturated sets of primes.
We introduce a new class of extensions of terms that consists in navigation strategies and insertion of contexts. We introduce an operation of combination on this class which is associative, admits a neutral element and so that each…
We define a new family of generalized Stirling permutations that can be interpreted in terms of ordered trees and forests. We prove that the number of generalized Stirling permutations with a fixed number of ascents is given by a natural…
We prove in this note that, for an alphabet with three letters, the set of first return to a given word in a set satisfying the tree condition is a basis of the free group.
Return words constitute a powerful tool for studying symbolic dynamical systems. They may be regarded as a discrete analogue of the first return map in dynamical systems. In this paper we investigate two abelian variants of the notion of…
We explore a physical model of ordered sums of integers as trains of rods. The trains for a fixed, possibly infinite, set of rod lengths naturally correspond to nodes in a tree; relations among finite linear recursions encoded in the…
We provide a semi-grammatical description of the set of normal proofs of positive formulae in minimal predicate logic, i.e. a grammar that generates a set of schemes, from each of which we can produce a finite number of normal proofs. This…
We describe an algorithm, implemented in Python, which can enumerate any permutation class with polynomial enumeration from a structural description of the class. In particular, this allows us to find formulas for the number of permutations…
We investigate the representation of the symmetric group afforded by the action on its conjugacy class of fixed point free involutions, over an algebraically closed field of finite characteristic p. We discuss the general form of the set of…
We study an alternative model of infinitary term rewriting. Instead of a metric on terms, a partial order on partial terms is employed to formalise convergence of reductions. We consider both a weak and a strong notion of convergence and…
We present a new lambda-calculus with explicit substitutions and named variables. Renaming of bound variables in this calculus is explicit (there is a special rewrite rule) and can be delayed. Contexts (environments) are not sets or lists…