Related papers: Garland Recurrences
Neural algorithmic reasoning (NAR) is an emerging field that seeks to design neural networks that mimic classical algorithmic computations. Today, graph neural networks (GNNs) are widely used in neural algorithmic reasoners due to their…
Phylogenetic networks are used in biology to represent evolutionary histories. The class of orchard phylogenetic networks was recently introduced for their computational benefits, without any biological justification. Here, we show that…
In this paper, we present a new algorithm for computing the linear recurrence relations of multi-dimensional sequences. Existing algorithms for computing these relations arise in computational algebra and include constructing structured…
Working with generating functions, the combinatorics of a recurrence relation can be expressed in a way that allows for more efficient calculation of the quantity. This is true of the Catalan numbers for an ordered binary tree…
After a period of decrease, interest in word alignments is increasing again for their usefulness in domains such as typological research, cross-lingual annotation projection, and machine translation. Generally, alignment algorithms only use…
Motivation coming from the study of affine Weyl groups, a structure of ranked poset is defined on the set of circular permutations in $S_n$ (that is, $n$-cycles). It is isomorphic to the poset of so-called admitted vectors, and to an…
This short note reports a master theorem on tight asymptotic solutions to divide-and-conquer recurrences with more than one recursive term: for example, T(n) = 1/4 T(n/16) + 1/3 T(3n/5) + 4 T(n/100) + 10 T(n/300) + n^2.
Reverse search is a convenient method for enumerating structured objects, that can be used both to address theoretical issues and to solve data mining problems. This method has already been successfully developed to handle unordered trees.…
During the last couple of years, Recurrent Neural Networks (RNN) have reached state-of-the-art performances on most of the sequence modelling problems. In particular, the "sequence to sequence" model and the neural CRF have proved to be…
Notions of guardedness serve to delineate the admissibility of cycles, e.g. in recursion, corecursion, iteration, or tracing. We introduce an abstract notion of guardedness structure on a symmetric monoidal category, along with a…
In 1882, Kronecker established that a given univariate formal Laurent series over a field can be expressed as a fraction of two univariate polynomials if and only if the coefficients of the series satisfy a linear recurrence relation. We…
Fibonacci sequence, generated by summing the preceding two terms, is a classical sequence renowned for its elegant properties. In this paper, leveraging properties of generalized Fibonacci sequences and formulas for consecutive sums of…
Garnets, known since the early stages of human civilization, have found important applications in modern technologies including magnetorestriction, spintronics, lithium batteries, etc. The overwhelming majority of experimentally known…
This paper establishes the exact comparison complexity of finding an element repeated $n$ times in a $2n$-element array containing $n+1$ distinct values, under the equality-comparison model with $O(1)$ extra space. We present a simple…
A structured approach for the Collatz conjecture is presented using just the odd integers that are, in turn, divided into categories based on the roles they play such as Starter, Intermediary and Terminal. The expression 4x+1 is used as a…
Divide-and-conquer functions satisfy equations in F(z),F(z^2),F(z^4)... Their generated sequences are mainly used in computer science, and they were analyzed pragmatically, that is, now and then a sequence was picked out for scrutiny. By…
For any triple given by a positive integer n, a finite group G, and a faithful representation V of G, one can describe a subspace arrangement whose intersection lattice is a generalized Dowling lattice in the sense of Hanlon. In this paper…
Initiated by Davis, Nelson, Petersen and Tenner (2018), the enumerative study of pinnacle sets of permutations has attracted a fair amount of attention recently. In this article, we provide a recurrence that can be used to compute…
A zig-zag order is like a directed path, only with alternating directions. A generating set of minimal size for the semigroup of all full transformations on a finite set preserving the zig-zag order was determined by Fenandes et al. in…
Generating trees are a useful technique in the enumeration of various combinatorial objects, particularly restricted permutations. Quite often the generating tree for the set of permutations avoiding a set of patterns requires infinitely…