Bijective Proofs of Gould's and Rothe's Identities

We first give a bijective proof of Gould's identity in the model of binary words. Then we deduce Rothe's identity from Gould's identity again by a bijection, which also leads to a double-sum extension of the $q$-Chu-Vandermonde formula.Comment: 4 page

Prendo la Parola in Questo Consesso Mondiale: A Multi-Genre 20th Century Corpus in the Political Domain

In this paper we present a multigenre corpus spanning 50 years of European history. It contains a comprehensive collection of Alcide De Gasperi’s public documents, 2,762 in total, written or transcribed between 1901 and 1954. The corpus comprises different types of texts, including newspaper articles, propaganda documents, official letters and parliamentary speeches. The corpus is freely available and includes several annotation layers, i.e. key-concepts, lemmas, PoS tags, person names and geo-referenced places, representing a high-quality ‘silver’ annotation. We believe that this resource can foster research in historical corpus analysis, stylometry and computational social science, among others

Identifying communicative functions in discourse with content types

Texts are not monolithic entities but rather coherent collections of micro illocutionary acts which help to convey a unitary message of content and purpose. Identifying such text segments is challenging because they require a fine-grained level of analysis even within a single sentence. At the same time, accessing them facilitates the analysis of the communicative functions of a text as well as the identification of relevant information. We propose an empirical framework for modelling micro illocutionary acts at clause level, that we call content types, grounded on linguistic theories of text types, in particular on the framework proposed by Werlich in 1976. We make available a newly annotated corpus of 279 documents (for a total of more than 180,000 tokens) belonging to different genres and temporal periods, based on a dedicated annotation scheme. We obtain an average Cohen’s kappa of 0.89 at token level. We achieve an average F1 score of 74.99% on the automatic classification of content types using a bi-LSTM model. Similar results are obtained on contemporary and historical documents, while performances on genres are more varied. This work promotes a discourse-oriented approach to information extraction and cross-fertilisation across disciplines through a computationally-aided linguistic analysis

Human and constructive proof of combinatorial identities: an example from Romik

International audienceIt has become customary to prove binomial identities by means of the method for automated proofs as developed by Petkovšek, Wilf and Zeilberger. In this paper, we wish to emphasize the role of "human'' and constructive proofs in contrast with the somewhat lazy attitude of relaying on "automated'' proofs. As a meaningful example, we consider the four formulas by Romik, related to Motzkin and central trinomial numbers. We show that a proof of these identities can be obtained by using the method of coefficients, a human method only requiring hand computations

A strip-like tiling algorithm

AbstractWe extend our previous results on the connection between strip tiling problems and regular grammars by showing that an analogous algorithm is applicable to other tiling problems, not necessarily related to rectangular strips. We find generating functions for monomer and dimer tilings of T- and L-shaped figures, holed and slotted strips, diagonal strips and combinations of them, and show how analogous results can be obtained by using different pieces

MultiEmotions-it: A new dataset for opinion polarity and emotion analysis for Italian

This paper1 presents a new linguistic resource for Italian, called MultiEmotions-It, containing comments to music videos and advertisements posted on YouTube and Facebook. These comments are manually annotated according to four different dimensions: i.e., relatedness, opinion polarity, emotions and sarcasm. For the annotation of emotions we adopted the Plutchik\u2019s model taking into account both basic and complex emotions, i.e. dyads

Iterative Processes Related to Riordan Arrays: The Reciprocation and the Inversion of Power Series

We point out how Banach Fixed Point Theorem, and the Picard successive approximation methods induced by it, allows us to treat some mathematical methods in Combinatorics. In particular we get, by this way, a proof and an iterative algorithm for the Lagrange Inversion Formula.Comment: 17 pages. We extend the results in the previuous version proving finally the Lagrange Inversion Formula via Banach Fixed Point Theore