On the invariants of a linear group of order 336
نویسنده
چکیده
The polynomial invariants of a certain classical linear group of order 336 arise naturally in studying error-correcting codes over GF(7). An incomplete description of these invariants was given by Maschke in 1893. With the aid of the Poincare series for this group, found by Edge in 1947, we complete Maschke's work by giving a unique representation for the invariants in terms of 12 basic invariants. A conjecture is made concerning the relationship between the Poincare series and the degrees of the basic invariants for any linear group. A partial answer to this conjecture, due to E. C. Dade, is given.
منابع مشابه
Signature submanifolds for some equivalence problems
This article concerned on the study of signature submanifolds for curves under Lie group actions SE(2), SA(2) and for surfaces under SE(3). Signature submanifold is a regular submanifold which its coordinate components are differential invariants of an associated manifold under Lie group action, and therefore signature submanifold is a key for solving equivalence problems.
متن کاملAlbertson energy and Albertson Estrada index of graphs
Let $G$ be a graph of order $n$ with vertices labeled as $v_1, v_2,dots , v_n$. Let $d_i$ be the degree of the vertex $v_i$ for $i = 1, 2, cdots , n$. The Albertson matrix of $G$ is the square matrix of order $n$ whose $(i, j)$-entry is equal to $|d_i - d_j|$ if $v_i $ is adjacent to $v_j$ and zero, otherwise. The main purposes of this paper is to introduce the Albertson ...
متن کاملIDEALS WITH (d1, . . . , dm)-LINEAR QUOTIENTS
In this paper, we introduce the class of ideals with $(d_1,ldots,d_m)$-linear quotients generalizing the class of ideals with linear quotients. Under suitable conditions we control the numerical invariants of a minimal free resolution of ideals with $(d_1,ldots,d_m)$-linear quotients. In particular we show that their first module of syzygies is a componentwise linear module.
متن کاملNew Improvement in Interpretation of Gravity Gradient Tensor Data Using Eigenvalues and Invariants: An Application to Blatchford Lake, Northern Canada
Recently, interpretation of causative sources using components of the gravity gradient tensor (GGT) has had a rapid progress. Assuming N as the structural index, components of the gravity vector and gravity gradient tensor have a homogeneity degree of -N and - (N+1), respectively. In this paper, it is shown that the eigenvalues, the first and the second rotational invariants of the GGT (I1 and ...
متن کاملNew Algorithm For Computing Secondary Invariants of Invariant Rings of Monomial Groups
In this paper, a new algorithm for computing secondary invariants of invariant rings of monomial groups is presented. The main idea is to compute simultaneously a truncated SAGBI-G basis and the standard invariants of the ideal generated by the set of primary invariants. The advantage of the presented algorithm lies in the fact that it is well-suited to complexity analysis and very easy to i...
متن کامل