Related papers: All Kronecker coefficients are reduced Kronecker c…

We introduce a variant of the $k$-nearest neighbor classifier in which $k$ is chosen adaptively for each query, rather than supplied as a parameter. The choice of $k$ depends on properties of each neighborhood, and therefore may…

One way to study the Kronecker coefficients is to focus on the Kronecker cone, which is generated by the triples of partitions corresponding to non-zero Kronecker coefficients. In this article we are interested in producing particular faces…

We present and prove closed form expressions for some families of binomial determinants with signed Kronecker deltas that are located along an arbitrary diagonal in the corresponding matrix. They count cyclically symmetric rhombus tilings…

We give a new formula for the Littlewood--Richardson coefficients in terms of peelable tableaux compatible with shuffle tableaux, in the same fashion as Remmel--Whitney rule. This gives an efficient way to compute generalized…

Binomial formulas for Schur polynomials and Jack polynomials were studied by Lascoux in 1978, and Kaneko, Okounkov--Olshanski and Lassalle in the 1990s. We prove that the associated binomial coefficients are monotone and derive some…

Let $G$ be the Klein Four-group and let $k$ be an arbitrary field of characteristic 2. A classification of indecomposable $kG$-modules is known. We calculate the relative cohomology groups $H_\{chi}^i(G,N)$ for every indecomposable…

Lie point symmetries of the 2+1-dimensional cubic Schr\"odinger equation to obtain new analytic solutions in a systematic manner. We present an analysis of the reduced ODEs, and in particular show that although the original equation is not…

We show that reducible braids which are, in a Garside-theoretical sense, as simple as possible within their conjugacy class, are also as simple as possible in a geometric sense. More precisely, if a braid belongs to a certain subset of its…

We present combinatorial operators for the expansion of the Kronecker product of irreducible representations of the symmetric group. These combinatorial operators are defined in the ring of symmetric functions and act on the Schur functions…

We describe a new algorithm that computes the minimal list of inequalities for the moment cone of any representation of a complex reductive group, with implementation details for two fundamental cases: the Kronecker cone (governing the…

Restriction of functions from a reductive p-adic group G to its compact subgroups defines an operator on the Hochschild and cyclic homology of the Hecke algebra of G. We study the commutation relations between this operator and others…

In this paper we show that the Poisson analogue of the Noether's Problem has a positive solution for essentially all finite symplectic reflection groups - the analogue of complex reflection groups in the symplectic world. Our proofs are…

We define an unreduced version of the e-controlled lower $K$-theoretic groups of Ranicki and Yamasaki, and Quinn. We show that the reduced versions of our groups coincide (in the inverse limit and its first derived, $\lim^1$) with those of…

We consider the relationship between the relative stable category of Benson, Iyengar, and Krause and the usual singularity category for group algebras with coefficients in a commutative noetherian ring. When the coefficient ring is…

The Clebsch--Gordan coefficients of the Kronecker products of the irreducible representations of the Quaternion Group Q8, of the Generalized Quaternion Groups Q16 and Q32, and of the factor group (Q32 X Q32)/{(1,1),(-1,-1)} are computed as…

After a short survey about Schroeder numbers and some generalizations which I call Schroeder-like numbers I study some q-analogues which have simple Hankel determinants.

We provide another approach to Friedland's result that the topological entropy $h$ of a symmetric nearest-neighbor subshift is computable. Instead of the previous algebraic technique, our approach is mostly combinatorial and involves only…

The Lichnerowicz conjecture asserts that all harmonic manifolds are either flat or locally symmetric spaces of rank 1. This conjecture has been proved by Z.I. Szabo for harmonic manifolds with compact universal cover. E. Damek and F. Ricci…

We discuss an extended easy quantum group formalism, with the Schur-Weyl theoretic Kronecker symbols being as general as possible, and allowed to take values in $\{-1,0,1\}$, and more generally in $\mathbb T\cup\{0\}$. Our study includes an…

We obtain the Plancherel theorem for the quotient of a simple Lie group of real rank one by a convex-cocompact discrete subgroup and its consequences for the spectrum of locally invariant differential operators on bundles over Kleinian…