Related papers: A note about words which coincide except in one po…
We consider fits to two or more datasets for which results from the sa me experiment share a common systematic uncertainty in addition to their individ ual statistical errors. This is important in extracting the maximum information from a…
Linguistic similarity is multi-faceted. For instance, two words may be similar with respect to semantics, syntax, or morphology inter alia. Continuous word-embeddings have been shown to capture most of these shades of similarity to some…
Word embedding models offer continuous vector representations that can capture rich contextual semantics based on their word co-occurrence patterns. While these word vectors can provide very effective features used in many NLP tasks such as…
Firstly, we provide a different proof of an important lemma in Buzzard and Calegari's work on slopes of overconvergent 2-adic modular forms via nonarchimedean linear Hodge-Newton decomposition. The lemma shows that two equivalent matrices…
The aim of this note is to share the observation that the set of elementary operations of Turing on lattice knots can be reduced to just one type of simple local switches.
We present an impossibility result, called a theorem about facts and words, which pertains to a general communication system. The theorem states that the number of distinct words used in a finite text is roughly greater than the number of…
This note presents an interesting counterexample to a basic covering problem.
This note corrects the paper \cite{ex}, where lattice sequences having exponentially large kissing numbers were constructed. However it was noted in \cite{dif} that the arguments in that paper are not sufficient. Here we correct the…
This paper provides effective methods for the polyhedral formulation of impartial finite combinatorial games as lattice games. Given a rational strategy for a lattice game, a polynomial time algorithm is presented to decide (i) whether a…
We investigate the equational theory of Kleene algebra terms with variable complements -- (language) complement where it applies only to variables -- w.r.t. languages. While the equational theory w.r.t. languages coincides with the language…
We consider colored compositions where only some parts are allowed different colors, depending on their locations in the composition. The counting sequences are obtained through generating functions. Connections to many other combinatorial…
In this paper we consider word equations with one variable (and arbitrary many appearances of it). A recent technique of recompression, which is applicable to general word equations, is shown to be suitable also in this case. While in…
On the premise that we are using passwords composed of multiple English words, we argue that using syntactically correct passphrases has no significant impact on the security in comparison to randomly arranged collections of words. We only…
In this paper, we extend the notion of Lyndon word to transfinite words. We prove two main results. We first show that, given a transfinite word, there exists a unique factorization in Lyndon words that are densely non-increasing, a…
In this paper, we propose a statistical test to determine whether a given word is used as a polysemic word or not. The statistic of the word in this test roughly corresponds to the fluctuation in the senses of the neighboring words a nd the…
We show how lattice paths and the reflection principle can be used to give easy proofs of unimodality results. In particular, we give a "one-line" combinatorial proof of the unimodality of the binomial coefficients. Other examples include…
These notes describe some results on dice comparisons when changing the numbers on the faces while the sum of all the face stay the same.
There are errors in the proof of the uniqueness of arithmetic subgroups of the smallest covolume. In this note we correct the proof, obtain certain results which were stated as a conjecture, and we give several remarks on further…
In this short note, we draw attention to a relation between two Horn polytopes which is proved in [Chenciner-Jim\'enez P\'erez] as the result on the one side of a deep combinatorial result in [Fomin,Fulton, Li,Poon], on the other side of a…
We develop the technique of reduced word manipulation to give a range of results concerning reduced words and permutations more generally. We prove a broad connection between pattern containment and reduced words, which specializes to our…