相关论文: Classification of Ramification Systems for Symmetr…

The problem of classification into symmetry integrable classes is solved for a family of second order nonlinear evolution equations labeled by arbitrary functions. Four nonequivalent symmetry integrable classes are thus obtained and the…

The derivation of the Hardy-Ramanujan-Rademacher formula for the number of partitions of $n$ is reviewed. Next, the steps for finding analogous formulas for certain restricted classes of partitions or overpartiitons is examined, bearing in…

We obtain an upper and lower bound for the number of reduced words for a permutation in terms of the number of braid classes and the number of commutation classes of the permutation. We classify the permutations that achieve each of these…

We give an explicit expression of the normalized characters of the symmetric group in terms of the contents of the partition labelling the representation.

Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…

We define a class of "algebraic" random matrix channels for which one can generically compute the limiting Shannon transform using numerical techniques and often enumerate the low SNR series expansion coefficients in closed form. We…

We present a new proof of the well known formula for the rank of the inclusion matrix by constructing a $k\mathcal{S}_n$-module spanned by the columns of this matrix and calculating its dimension.

The cohomology ring of a finite group, with coefficients in a finite field, can be computed by a machine, as Carlson has showed. Here "compute" means to find a presentation in terms of generators and relations, and involves only the…

If $G$ is a transitive group of degree $n$ having a string C-group of rank $r\geq (n+3)/2$, then $G$ is necessarily the symmetric group $S_n$. We prove that if $n$ is large enough, up to isomorphism and duality, the number of string…

Using limit linear series and a result controlling degeneration from separable maps to inseparable maps, we give a formula for the number of self-maps of the projective line with ramification to order e_i at general points P_i, in the case…

The ramified Siegel series is an important factor that appears in the Fourier coefficient of the Siegel Eisenstein series.Many formulas for the ramified Siegel series under various conditions are already known.However, an explicit formula…

For a given abelian group G, we classify the isomorphism classes of G-gradings on the simple restricted Lie algebras of types W(m;1) and S(m;1) (m>=2), in terms of numerical and group-theoretical invariants. Our main tool is automorphism…

Motivated by questions from program transformations, eight notions of isomorphisms between term rewriting systems are defined, analysed, and classified. The notions include global isomorphisms, where the renaming of variables and function…

We propose an approach for the computation of multi-parameter families of Galois extensions with prescribed ramification type. More precisely, we combine existing deformation and interpolation techniques with recently developed strong tools…

We find a formula for the number of permutations of $[n]$ that have exactly $s$ runs up and down. The formula is at once terminating, asymptotic, and exact.

For a rational prime $p\neq 2$, we compute the sequence of ramification groups of a Galois, radical and finite extension $L/F$ where $F/\mathbb{Q}_p$ is an unramified finite extension. First, we compute it in the case where the exponent of…

We obtain explicit formulas for the number of non-isomorphic elliptic curves with a given group structure (considered as an abstract abelian group). Moreover, we give explicit formulas for the number of distinct group structures of all…

Let $n$ be a positive integer, and let $R$ be a (possibly infinite dimensional) finitely presented algebra over a computable field of characteristic zero. We describe an algorithm for deciding (in principle) whether $R$ has at most finitely…

We give a new formula for the values of an irreducible character of the symmetric group S_n indexed by a partition of rectangular shape. Some observations and a conjecture are given concerning a generalization to arbitrary shapes.

The class of all quasigroups is covered by six classes: the class of all asymmetric quasigroups and five varieties of quasigroups (commutative, left symmetric, right symmetric, semi-symmetric and totally symmetric). Each of these classes is…