Related papers: On the Schaper Number of Partitions

Let $A_{t,k}(n)$ denote the number of partition $k$-tuples of $n$ where each partition is $t$-core. In this paper, we establish formulas of $A_{t,k}(n)$ for some values of $t$ and $k$ by employing the method of modular forms, which extends…

We study separability criteria in multipartite quantum systems of arbitrary dimensions by using the Bloch representation of density matrices. We first derive the norms of the correlation tensors and obtain the necessary conditions for…

Let k be an algebraically closed field of characteristic p>2. We compute the Weyl filtration multiplicities in indecomposable tilting modules and the decomposition numbers for the symplectic group over k in terms of cap-curl diagrams under…

We study the enumeration problem of higher dimensional partitions, a natural generalisation of classical integer partitions. We show that their counting problem is equivalent to the enumeration of simpler classes of higher dimensional…

In this paper, a matrix is said to be prime if the row and column of this matrix are both prime numbers. We establish various necessary and sufficient conditions for developing matrices into the sum of tensor products of prime matrices. For…

Prior to the parallel solution of a large linear system, it is required to perform a partitioning of its equations/unknowns. Standard partitioning algorithms are designed using the considerations of the efficiency of the parallel…

We calculate the partition function for "composite particles". For any finite number of states d, and in the following two cases: 1)all states have the same energy, 2)the energy is linearly distributed over the states, we transform the…

A univariate polynomial f over a field is decomposable if f = g o h = g(h) for nonlinear polynomials g and h. It is intuitively clear that the decomposable polynomials form a small minority among all polynomials over a finite field. The…

We obtain a closed formula for the $v$-decomposition numbers $d_{\lambda\mu}(v)$ arising from the canonical basis of the Fock space representation of $U_v(\hat{\mathfrak{sl}}_e)$, where the partition $\lambda$ is obtained from $\mu$ by…

A precise estimation of the computational complexity in Shor's factoring algorithm under the condition that the large integer we want to factorize is composed by the product of two prime numbers, is derived by the results related to number…

A partition of degree $n$ is a decomposition $n=i_1+i_2+\dots+i_q$, where ${i_1,i_2,\dots,i_q}$ are positive integers called the parts of the partition. Let $\lambda>0$ be an integer. The partition is said to be a $\lambda$--partition if…

We consider the measure on multiple chordal Schramm-Loewner evolution ($SLE_\kappa$) curves. We establish a derivative estimate and use it to give a direct proof that the partition function is $C^2$ if $\kappa<4$.

Constructive algorithms, requiring no more than $2\times 2$ matrix manipulations, are provided for finding the entries of the positive definite factor in the polar decomposition of matrices in sixteen groups preserving a bilinear form in…

In recent joint work with Wang, we have constructed graded Specht modules for cyclotomic Hecke algebras. In this article, we prove a graded version of the Lascoux-Leclerc-Thibon conjecture, describing the decomposition numbers of graded…

This paper concerns cheaply computable formulas and bounds for the condition number of the TLS problem. For a TLS problem with data $A$, $b$, two formulas are derived that are simpler and more compact than the known results in the…

We construct a new family of homomorphisms from Specht modules into Foulkes modules for the symmetric group. These homomorphisms are used to give a combinatorial description of the minimal partitions (in the dominance order) which label…

In this paper, we calculate an exact formula for the number of partitions of a natural number $n$, where the largest part is even and no odd parts appears more than two times. The generating functions of the number of these partitions is a…

Schur duality decomposes many copies of a quantum state into subspaces labeled by partitions, a decomposition with applications throughout quantum information theory. Here we consider applying Schur duality to the problem of distinguishing…

We investigate integral forms of simple modules of symmetric groups over fields of characteristic $0$ labelled by hook partitions. Building on work of Plesken and Craig, for every odd prime $p$, we give a set of representatives of the…

Using a specific form of the triple product identity, polygonal number identities are stated. Further number identities are examined that can be considered identities related to modular sets of numbers. The identities can be used to give…