Related papers: Further results on staircase (cyclic) words

We say a string has a cadence if a certain character is repeated at regular intervals, possibly with intervening occurrences of that character. We call the cadence anchored if the first interval must be the same length as the others. We…

If a string is cyclically shifted it will re-appear after a certain number of shifts, which will be called its order. We solve the problem of how many strings exist with a given order. This problem arises in the context of quantum mechanics…

Statistics pedagogy values using a variety of examples. Thanks to text resources on the Web, and since statistical packages have the ability to analyze string data, it is now easy to use language-based examples in a statistics class. Three…

In this paper, we focus on the enumeration of permutations by number of cyclic occurrence of peaks and valleys. We find several recurrence relations involving the number of permutations with a prescribed number of cyclic peaks, cyclic…

Given a set $F$ of words, one associates to each word $w$ in $F$ an undirected graph, called its extension graph, and which describes the possible extensions of $w$ on the left and on the right. We investigate the family of sets of words…

Given a random text over a finite alphabet, we study the frequencies at which fixed-length words occur as subsequences. As the data size grows, the joint distribution of word counts exhibits a rich asymptotic structure. We investigate all…

Multiplicative cascades have been introduced in turbulence to generate random or deterministic fields having intermittent values and long-range power-law correlations. Generally this is done using discrete construction rules leading to…

Prompted models have demonstrated impressive few-shot learning abilities. Repeated interactions at test-time with a single model, or the composition of multiple models together, further expands capabilities. These compositions are…

Convection structures in binary fluid mixtures are investigated for positive Soret coupling in the driving regime where solutal and thermal contributions to the buoyancy forces compete. Bifurcation properties of stable and unstable…

Functional dynamics, introduced in a previous paper, is analyzed, focusing on the formation of a hierarchical rule to determine the dynamics of the functional value. To study the periodic (or non-fixed) solution, the functional dynamics is…

A reformulation of the path length of binary search trees is given in terms of permutations, allowing to extend the definition to the instance of words, where the letters are obtained by independent geometric random variables (with…

This work is a continuation of some recent articles presenting enumerative results for Catalan words avoiding one or a pair of consecutive or classical patterns of length $3$. More precisely, we provide systematically the bivariate…

Surprisal theory has provided a unifying framework for understanding many phenomena in sentence processing (Hale, 2001; Levy, 2008a), positing that a word's conditional probability given all prior context fully determines processing…

We give a new proof of the butterfly theorem, based on the use of several expressions involving the scale factor between the two wings.

The syntactic structure of a sentence can be represented as a graph, where vertices are words and edges indicate syntactic dependencies between them. In this setting, the distance between two linked words is defined as the difference…

Written language is a complex communication signal capable of conveying information encoded in the form of ordered sequences of words. Beyond the local order ruled by grammar, semantic and thematic structures affect long-range patterns in…

A turn in a computation of a pushdown automaton is a switch from a phase in which the height of the pushdown store increases to a phase in which it decreases. Given a pushdown or one-counter automaton, we consider, for each string in its…

The multiple zeta values are generalizations of the values of the Riemann zeta function at positive integers. They are known to satisfy a number of relations, among which are the cyclic sum formula. The cyclic sum formula can be stratified…

It is proved that the set of geodesic circles in two dimensions may be given a variational description and the explicit form of it is presented. In the limit case of the Euclidean geometry a certain claim of uniqueness of such description…

We count the number of lattice paths lying under a cyclically shifting piecewise linear boundary of varying slope. Our main result extends well known enumerative formulae concerning lattice paths, and its derivation involves a classical…