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We introduce bijections between families of rooted maps with unfixed genus and families of so-called blossoming trees endowed with an arbitrary forward matching of their leaves. We first focus on Eulerian maps with controlled vertex…
Whether explicit or implicit, sets are a critical part of many pieces of software. As a result, it is necessary to develop abstractions of sets for the purposes of abstract interpretation, model checking, and deductive verification.…
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…
Two subfamilies of Motzkin paths, with the same numbers of up, down, horizontal steps were known to be equinumerous with ternary trees and related objects. We construct a bijection between these two families that does not use any auxiliary…
I present a simple algorithm for enumerating the trees generated by a Context Free Grammar (CFG). The algorithm uses a pairing function to form a bijection between CFG derivations and natural numbers, so that trees can be uniquely decoded…
The enumeration of linear $\lambda$-terms has attracted quite some attention recently, partly due to their link to combinatorial maps. Zeilberger and Giorgetti (2015) gave a recursive bijection between planar linear normal $\lambda$-terms…
The arithmetic of natural numbers has a natural and simple encoding within sets, and the simplest set whose structure is not that of any natural number extends this set-theoretic representation to positive and negative integers. The…
We show that there is a bijection between the subtoposes of the classifying topos of a geometric theory T over a signature L and the closed geometric theories over L which are `quotients' of the theory T; next, we analyze how classical…
This paper contains a description of a connection between the matching arrangement and the matching polyhedron. A bijection between regions of the matching arragement and LP-orientations of the matching polyhedron is constructed. This…
In this paper we illuminate some algebraic-combinatorial structure underlying the second order networks (SONETS) random graph model of Nykamp, Zhao and collaborators. In particular we show that this algorithm is deeply connected with a…
We here give polynomial realizations of various Hopf algebras or bialgebras on Feynman graphs, graphs, posets or quasi-posets, that it to say injections of these objects into polynomial algebras generated by an alphabet. The alphabet here…
We define a bijection between triangulations of a convex polygon and $312$-avoiding permutations through the process of "ear-clipping". This bijection is then used to obtain a bijection between polygon dissections and a certain class of…
We unify and extend previous bijections on plane quadrangulations to bipartite and quasibipartite plane maps. Starting from a bipartite plane map with a distinguished edge and two distinguished corners (in the same face or in two different…
We endow the category of bialgebras over a pair of operads in distribution with a cofibrantly generated model category structure. We work in the category of chain complexes over a field of characteristic zero. We split our construction in…
Bias in textual data can lead to skewed interpretations and outcomes when the data is used. These biases could perpetuate stereotypes, discrimination, or other forms of unfair treatment. An algorithm trained on biased data may end up making…
Logical frameworks based on intuitionistic or linear logics with higher-type quantification have been successfully used to give high-level, modular, and formal specifications of many important judgments in the area of programming languages…
Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices made in the construction of the…
Dictionary learning is a cornerstone of image classification. We set out to address a longstanding challenge in using dictionary learning for classification; that is to simultaneously maximise the discriminability and…
We evaluate combinatorially certain connection coefficients of the symmetric group that count the number of factorizations of a long cycle as a product of three permutations. Such factorizations admit an important topological interpretation…
Hierarchical Text Classification (HTC) is a challenging task where a document can be assigned to multiple hierarchically structured categories within a taxonomy. The majority of prior studies consider HTC as a flat multi-label…