Related papers: Generalized hook lengths in symbols and partitions
We introduce and systematically develop two classes of discrete integrable operators: those with $2\times 2$ matrix kernels and those possessing general differential kernels, thereby generalizing the discrete analogue previously studied. A…
In this paper we describe how representation theory of groups can be used to shorten the derivation of two loop partition functions in string theory, giving an intrinsic description of modular forms appearing in the results of D'Hoker and…
In the present article, real number representations, that are generalizations of classical positive and alternating representations of numbers, are introduced and investigated. The main metric relation, properties of cylinder sets are…
We prove new concentration estimates for random variables that are functionals of a Poisson measure defined on a general measure space. Our results are specifically adapted to geometric applications, and are based on a pervasive use of a…
Consider a string of $n$ positions, i.e. a discrete string of length $n$. Units of length $k$ are placed at random on this string in such a way that they do not overlap, and as often as possible, i.e. until all spacings between neighboring…
The main purpose of this paper is to study the hybrid mean value problem involving generalized Dedekind sums, generalized Hardy sums and Kloosterman sums, and give some exact computational formulae for them by using the properties of Gauss…
We provide a deterministic data summarization algorithm that approximates the mean $\bar{p}=\frac{1}{n}\sum_{p\in P} p$ of a set $P$ of $n$ vectors in $\REAL^d$, by a weighted mean $\tilde{p}$ of a \emph{subset} of $O(1/\eps)$ vectors,…
Graph code is a linear code obtained from linear codes $C$ and a certain bipartite graph G. In this paper, I propose an expansion of the definition of graph code to general $l$-partite, and give its lower bound of minimum distance. I also…
For a block B of a finite group G there are well-known orthogonality relations for the generalized decomposition numbers. We refine these relations by expressing the generalized decomposition numbers with respect to an integral basis of a…
Xu and Wu (2001) defined the \emph{generalized wordlength pattern} $(A_1, ..., A_k)$ of an arbitrary fractional factorial design (or orthogonal array) on $k$ factors. They gave a coding-theoretic proof of the property that the design has…
A natural problem in combinatorial rigidity theory concerns the determination of the rigidity or flexibility of bar-joint frameworks in $\mathbb{R}^d$ that admit some non-trivial symmetry. When $d=2$ there is a large literature on this…
We derive the asymptotic formula for $p_n(N,M)$, the number of partitions of integer $n$ with part size at most $N$ and length at most $M$. We consider both $N$ and $M$ are comparable to $\sqrt{n}$. This is an extension of the classical…
Firstly, we give a formula on the generalized Hamming weight of linear codes constructed generically by defining sets. Secondly, by choosing properly the defining set we obtain a class of cyclotomic linear codes and then present two…
We prove the existence of infinite classes of cyclic G-decompositions of the complete multipartite graph, G being a caterpillar, a hairy cycle or a cycle. All the results are obtained by the construction of d-divisible $\alpha$-labelings of…
Generalizing the notion of split graphs to uniform hypergraphs, we prove that the class of these hypergraphs can be characterized by a finite list of excluded induced subhypergraphs. We show that a characterization by generalized degree…
Assuming the generalized Riemann hypothesis and a bound for the negative discrete moments of the Riemann zeta function (resp. Dirichlet $L$-functions), we prove the existence of a logarithmic limiting distribution for the normalized partial…
Marginal polytopes are important geometric objects that arise in statistics as the polytopes underlying hierarchical log-linear models. These polytopes can be used to answer geometric questions about these models, such as determining the…
Let $Y$ be a projective submanifold of the total space of the inverse of a very ample line bundle $\pi:L^{-1}\rightarrow B$ over a projective manifold $B$. Any section of $L^{-1}\rightarrow B$ is isomorphic to $B$ and the Hodge numbers of…
We generalize the Harary-Sachs theorem to $k$-uniform hypergraphs: the codegree-$d$ coefficient of the characteristic polynomial of a uniform hypergraph ${\cal H}$ can be expressed as a weighted sum of subgraph counts over certain…
Using the Markov distance and Ptolemy inequality introduced by Lee-Li-Rabideau-Schiffler \cite{LLRS}, we completely determine the monotonicity of the generalized Markov numbers along the lines of a given slope.