Related papers: Combinatorial equivalence of separable elements in…

A permutation class is splittable if it is contained in the merge of two of its proper subclasses. We characterise the unsplittable subclasses of the class of separable permutations both structurally and in terms of their bases.

We determine the sharp asymptotic scale of the probability that two uniformly random permutations are comparable in weak Bruhat order, showing that $\mathbb{P}(\sigma_1 \preceq_W \sigma_2)=\exp\Bigl(\bigl(-\tfrac12+o(1)\bigr)\,n\log…

We classify the spherical birational sheets in a complex simple simply-connected algebraic group. We use the classification to show that, when $G$ is a connected reductive complex algebraic group with simply-connected derived subgroup, two…

We give a combinatorial construction of an ordered semiring A, and show that it can be identified with a certain subquotient of the semiring of p-local Bousfield classes, containing almost all of the classes that have previously been named…

Let n>0 be an integer and let B_{n} denote the hyperoctahedral group of rank n. The group B_{n} acts on the polynomial ring Q[x_{1},...,x_{n},y_{1},...,y_{n}] by signed permutations simultaneously on both of the sets of variables…

Let $A$ be a separable $C^*$-algebra and $B$ a stable $C^*$-algebra containing a strictly positive element. We show that the group $\Ext(SA,B)$ of unitary equivalence classes of extensions of $SA$ by $B$, modulo the extensions which are…

Following the method of combinatorial telescoping for alternating sums given by Chen, Hou and Mu, we present a combinatorial telescoping approach to partition identities on sums of positive terms. By giving a classification of the…

For a commutative ring $A$, we have the category of (bounded-below) chain complexes of $A$-modules $Ch_{+}(A\mymod)$, a closed symmetric monoidal category with a compatible stable Quillen model structure. The associated homotopy category is…

For any graded commutative noetherian ring, where the grading group is abelian and where commutativity is allowed to hold in a quite general sense, we establish an inclusion-preserving bijection between, on the one hand, the twist-closed…

The construction of joins and secant varieties is studied in the combinatorial context of monomial ideals. For ideals generated by quadratic monomials, the generators of the secant ideals are obstructions to graph colorings, and this leads…

Let $\mathscr{C}$ be an additive subcategory of left $\Lambda$-modules, we establish relations of the orthogonal classes of $\mathscr{C}$ and (co)res $\widetilde{\mathscr{C}}$ under separable equivalences. As applications, we obtain that…

We study the structure of separable elements in bipartite C$^{\ast}$-algebras, focusing on the existence and size of a separable neighbourhood around the identity element. While this phenomenon is well understood in the finite-dimensional…

In this paper, we connect two types of representations of a permutation $\sigma$ of the finite field $\F_q$. One type is algebraic, in which the permutation is represented as the composition of degree-one polynomials and $k$ copies of…

Recently, Schneider and Schneider defined a new class of partitions called sequentially congruent partitions, in which each part is congruent to the next part modulo its index, and they proved two partition bijections involving these…

We give a characterization of the sets of objects of the derived category of a block of a finite group algebra (or other symmetric algebra) that occur as the set of images of simple modules under an equivalence of derived categories. We…

Binary Parseval frames share many structural properties with real and complex ones. On the other hand, there are subtle differences, for example that the Gramian of a binary Parseval frame is characterized as a symmetric idempotent whose…

We present a simple bijection between permutation matrices and descending plane partitions without special parts. This bijection is already mentioned in work of P. Lalonde (without giving the details); it involves the inversion words of…

We prove a conjecture dating back to a 1978 paper of D.R.\ Musser~\cite{musserirred}, namely that four random permutations in the symmetric group $\mathcal{S}_n$ generate a transitive subgroup with probability $p_n > \epsilon$ for some…

We study the set $\sncb (p,q)$ of annular non-crossing permutations of type B, and we introduce a corresponding set $\ncb (p,q)$ of annular non-crossing partitions of type B, where $p$ and $q$ are two positive integers. We prove that the…

We consider the monomial expansion of the $q$-Whittaker and modified Hall-Littlewood polynomialsarising from specialization of the modified Macdonald polynomial. The two combinatorial formulas for the latter due to Haglund, Haiman, and…