Related papers: Bruhat operads
The purpose of this exposition is to compare the constructions of classical nonsymmetric operads (and their algebras) to that of the globular operads of Leinster and Batanin. It is hoped that, through this comparison, understanding algebras…
We compute all liftings of braidings of unidentified types ufo(7) and ufo(8). Some of these examples had been previously computed by Helbig. We also present a list of examples of liftings of modular type br(2,a).
We study order units in the real group ring and the augmentation ideal, as well as in matrix algebras. We identify an infinite family of order units in the powers of the augmentation ideal, that includes the Laplacian, and show that these…
In this paper, I introduce a new generalization of the concept of an operad, further generalizing the concept of an opetope introduced by Baez and Dolan, who used this for the definition of their version of non-strict $n$-categories.…
Rigorous modelling of natural and industrial systems still conveys various challenges related to abstractions, methods to proceed with and easy-to-use tools to build, compose and reason on models. Operads are mathematical structures that…
We propose an algorithm generating planar networks which structure resembles a hierarchical structure of desiccation crack patterns.
We describe a conjecture on the algebra of higher cohomology operations which leads to the computations of the differentials in the Adams spectral sequence. For this we introduce the notion of an n-th order track category which is suitable…
In this paper, we give some interesting identities of higher-order Bernoulli, Frobenius-Euler and Euler polynomials arising from umbral calculus. From our method of this paper, we can derive many interesting identities of special…
We present some new results about the resonance varieties of matroids and hyperplane arrangements. Though these have been the objects of ongoing study, most work so far has focussed on cohomological degree 1. We show that certain phenomena…
We prove that split reductive BT group schemes over a higher dimensional base are {\em affine}. Our method also gives a new construction of higher BT-group schemes more general than parahoric ones. The new ingredients are an extension of…
In this paper we answer a question raised in [25], Sec. 4, by showing that the genus zero moduli operad $\{\bar{M}_{0,n+1}\}$ can be endowed with natural descent data that allow it to be considered as the lift to ${\rm Spec}\,\Z$ of an…
We give a description of unital operads in a symmetric monoidal category as monoids in a monoidal category of unital $\Lambda$-sequences. This is a new variant of Kelly's old description of operads as monoids in the monoidal category of…
We study the action on the Bruhat-Tits tree of unit groups of maximal orders in certain quaternion algebras over $\mathbb{F}_q(T)$ and discuss applications to arithmetic geometry and group theory.
In various subjects including mathematics, one can hope to use mathematical thinking well when the right kinds of algebraic structure to consider can be discovered or spotted. Therefore, it would help to understand kinds of algebraic…
A theory of higher rank multiresolution analysis is given in the setting of abelian multiscalings. This theory enables the construction, from a higher rank MRA, of finite wavelet sets whose multidilations have translates forming an…
Higher-derivative analogues of multidimensional conformal particle and many-body conformal mechanics are constructed. Their Newton-Hooke counterparts are derived by applying appropriate coordinate transformations.
We study the link between the degree growth of integrable birational mappings of order higher than two and their singularity structures. The higher order mappings we use in this study are all obtained by coupling mappings that are…
We prove the conjecture that the higher Tamari orders of Dimakis and M\"uller-Hoissen coincide with the first higher Stasheff--Tamari orders. To this end, we show that the higher Tamari orders may be conceived as the image of an…
The associative operad is a certain algebraic structure on the sequence of group algebras of the symmetric groups. The weak order is a partial order on the symmetric group. There is a natural linear basis of each symmetric group algebra,…
We investigate the poset of strata of a Schubert-like stratification of certain natural compactification of the space of hermitian $n\times n$ matrices. We prove that this poset is a modular ortholattice, we compute its M\"{o}bius function…