Related papers: The 2-associahedra are Eulerian

The Bruhat operads from \cite{KS} are equipped with a structure of operads with multiplication.

Some simple nonlinear recursions which can be completely managed are identified and the behaviour of all their solutions is ascertained.

The Eulerian triangle is a classical array of combinatorial numbers defined by a linear recursion. The associated boundary problem asks one to find all extreme nonnegative solutions to a dual recursion. Exploiting connections with random…

Using Eulerian and Euler numbers, we establish congruences concerning sums involving harmonic numbers, tangent numbers and Genocchi numbers.

For the chiral oscillator described by a second order and degenerate Lagrangian with special Euclidean group of symmetries, we show, by cotangent bundle Hamiltonian reduction, that reduced equations are Lie-Poisson on dual of oscillator…

In this note we provide a direct proof of the complete classification of conformally flat isoparametric submanifolds of Euclidean space.

We introduce the notion of omni-Lie 2-algebra, which is a categorification of Weinstein's omni-Lie algebras. We prove that there is a one-to-one correspondence between strict Lie 2-algebra structures on 2-sub-vector spaces of a 2-vector…

We demonstrate the common bihamiltonian nature of several integrable systems. The first one is an elliptic rotator that is an integrable Euler-Arnold top on the complex group GL(N) for any $N$, whose inertia ellipsiod is related to a choice…

We investigate the relation between pluri-Lagrangian hierarchies of $2$-dimensional partial differential equations and their variational symmetries. The aim is to generalize to the case of partial differential equations the recent findings…

We find all polyhedral graphs such that their complements are still polyhedral. These turn out to be all self-complementary.

In this note we give the Kolyvagin recursion in cyclotomic Euler systens a new and universal interpretation with the help of the double complex method introduced by Anderson and further developed by Das and Ouyang. Namely, we show that the…

In this paper we introduce multiplicative Dirac structures on Lie groupoids, providing a unified framework to study both multiplicative Poisson bivectors (i.e., Poisson group(oid)s) and multiplicative closed 2-forms (e.g., symplectic…

By applying the idea of viewing the octonions as an associative algebra in certain tensor categories, or more precisely as a twisted group algebra by a 2-cochain, we show that the octonions form an Azumaya algebra in some suitable braided…

Recently, symmetric categorical groups are used for the study of the Brauer groups of symmetric monoidal categories. As a part of these efforts, some algebraic structures of the 2-category of symmetric categorical groups $\mathrm{SCG}$ are…

We present alternative postulates for Euclidean geometry whose merit is that they lead to a new class of invariants and associated geometries for real finite-dimensional unital associative algebras.

We define 2-gerbes bound by complexes of braided group-like stacks. We prove a classification result in terms of hypercohomology groups with values in abelian crossed squares and cones of morphisms of complexes of length 3. We give an…

Smooth and proper dg-algebras have an Euler class valued in the Hochschild homology of the algebra. This Euler class is worthy of this name since it satisfies many familiar properties including compatibility with the familiar pairing on the…

In this note we prove Yosida duality --- that is: the category of compact Hausdorff spaces with continuous maps is dually equivalent to the category of uniformly complete Archimedean Riesz spaces with distinguished units and unit-preserving…

We consider a family of K\"ahler structures on products of 2-spheres, arising from complex Bott manifolds. These are obtained via iterated $\mathbb P^1$-bundle constructions, generalizing the classical Hirzebruch surfaces. We show that the…

We show that two properly embedded compact surfaces in an orientable 4-manifold are cobordant if and only if they are $\mathbb{Z}/2$-homologous and either the 4-manifold has boundary or the surfaces have the same normal Euler number. If the…