This paper defines the algebraic structure of tracial post-Lie-Rinehart algebras and describes the free object in this category. Post-Lie-Rinehart algebras is a generalisation of pre-Lie-Rinehart algebras, and of post-Lie algebroids.
We give a pattern-avoidance characterization of $w \in S_n$ such that the Schubert polynomial $\mathfrak{S}_w$ is a standard elementary monomial. This characterization tells us which quantum Schubert polynomials are easiest to compute. We solve a similar problem for complete homogeneous monomials.
In this paper, we determine all connected net-regular strongly regular signed graphs with degree 5. There are five and two strongly regular signed graphs with net-degree 3 and 1, respectively.
In this paper new Steiner systems $S(2,6,111)$, $S(2,6,121)$, $S(2,6,126)$, $S(2,7,169)$, $S(2,7,175)$ and possibly others with point-transitive (commutative except $S(2,6,111)$ case) automorphism groups are introduced.
AbstractWe consider two preorder-enriched categories of ordered partial combinatory algebras: OPCA, where the arrows are functional (i.e., projective) morphisms, and OPCA†, where the arrows are applicative morphisms. We show that OPCA has small products and finite biproducts, and that OPCA† has finite coproducts, all in a suitable 2-categorical sense. On the other hand, OPCA† lacks all nontrivial binary products. We deduce from this that the pushout, over Set, of two nontrivial realizability toposes is never a realizability topos. In contrast, we show that nontrivial subtoposes of realizability toposes are closed under pushouts over Set.
We introduce and study a subring $\mathcal{SC}$ of $\mathbb Z[\mathrm{SL}\_2(\mathbb F\_q)]$ obtained by summing elements of $\mathrm{SL}\_2(\mathbb F\_q)$ according to their support. The ring $\mathcal SC$ can be used for the construction of several association schemes.
Using only a symmetric p-core partition and p-quotient, we give an explicit formula for the set of diagonal hook lengths of the associated symmetric partition.
We extend Federer’s co-area formula to mappings f f belonging to the Sobolev class W 1 , p ( R n ; R m ) W^{1,p}(\mathbb {R}^n;\mathbb {R}^m) , 1 ≤ m > n 1 \le m > n , p > m p>m , and more generally, to mappings with gradient in the Lorentz space L m , 1 ( R n ) L^{m,1}(\mathbb {R}^n) . This is accomplished by showing that the graph of f f in R n + m \mathbb {R}^{n+m} is a Hausdorff n n -rectifiable set.