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We study the satisfiability problem for the fluted fragment extended with transitive relations. We show that the logic enjoys the finite model property when only one transitive relation is available. On the other hand we show that 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…

In this paper we introduce and study a class of tableaux which we call permutation tableaux; these tableaux are naturally in bijection with permutations, and they are a distinguished subset of the Le-diagrams of Alex Postnikov. The…

Fluid-mediated interactions between particles in a vibrating fluid lead to both long range attraction and short range repulsion. The resulting patterns include hexagonally ordered micro-crystallites, time-periodic structures, and chaotic…

We prove generalized versions of some conjectures of Joel Lewis on the number of alternating permutations avoiding certain patterns. Our main tool is the perhaps surprising observation that a classic bijection on pattern avoiding…

We use model theoretic techniques to construct explicit first-order axiomatizations for the classes of posets that can be represented as systems of sets, where the order relation is given by inclusion, and existing meets and joins of…

The Eilenberg correspondence relates varieties of regular languages to pseudovarieties of finite monoids. Various modifications of this correspondence have been found with more general classes of regular languages on one hand and classes of…

We discuss both simple and more subtle connections between the numbers of permutations and full cycles with some restrictions,in particular, between the numbers of permutations and full cycles with prescribed up-down structure.

We define and study odd analogues of classical geometric and combinatorial objects associated to permutations, namely odd Schubert varieties, odd diagrams, and odd inversion sets. We show that there is a bijection between odd inversion sets…

We introduce a framework to identify Fluctuation Relations for vector-valued observables in physical systems evolving through a stochastic dynamics. These relations arise from the particular structure of a suitable entropic functional and…

We consider a model of random permutations of the sites of the cubic lattice. Permutations are weighted so that sites are preferably sent onto neighbors. We present numerical evidence for the occurrence of a transition to a phase with…

We consider a large family of equivalence relations on permutations in Sn that generalise those discovered by Knuth in his study of the Robinson-Schensted correspondence. In our most general setting, two permutations are equivalent if one…

In this paper we compute the multiplicities appearing in the ${\overline{\mathbb{F}}_\ell}$-modular theta correspondence in type II over a non-archimedean field $\mathrm{F}$, where $\ell$ is a prime not dividing the residue cardinality of…

Let S_n(321) (respectively, S_n(132)) denote the set of all permutations of {1,2,...,n} that avoid the pattern 321 (respectively, the pattern 132). Elizalde and Pak gave a bijection Theta from S_n(321) to S_n(132) that preserves the numbers…

We construct a refined bijection $\phi$ between alternating permutations and 0-1-2 increasing trees with degree at most 2. It satisfies that the first element of alternating permutation $\pi$ is equal to the first vertex in $\phi(\pi)$ in…

A now-classical cyclic extension of the descent set of a permutation has been introduced by Klyachko and Cellini. Following a recent axiomatic approach to this notion, it is natural to ask which sets of permutations admit such an extension.…

Configurations are necklaces with prescribed numbers of red and black beads. Among all possible configurations, the regular one plays an important role in many applications. In this paper, several aspects of regular configurations are…

We prove a remarkable combinatorial symmetry in the number of spanning configurations in site percolation: for a large class of lattices, the number of spanning configurations with an odd or even number of occupied sites differs by $\pm 1$.…

We prove that there is a bijection between the families of regular and non-regular operator monotone functions. As an application we give a new proof of the operator monotonicity of a certain class of functions related to…

Coherent sets of almost desirable gambles and credal sets are known to be equivalent models. That is, there exists a bijection between the two collections of sets preserving the usual operations, e.g. conditioning. Such a correspondence is…