Mathematics - Combinatorics05-0005Axx05ExxA survey written for the upcoming "Handbook of Enumerative Combinatorics".doi:10.1201/b18255-3Ardila, FedericoEprint ArxivF. Ardila, Algebraic and geometric methods in enumerative combinatorics. Handbook of Enumerative Combinatorics, ed. M. Bona, Chapman and...
So one basic approach in combinatorics is to investigate combinatorial objects by using linear algebraic parameters (ranks over various fields, spectrum, Smith normal forms, etc.) of their corresponding matrices. In this talk, we will look at some successful examples of this approach; some examples...
Eigenvalue methods also play a crucial role in this paper, but the situation is more complex and interesting for two reasons. First of all, the adjacency matrix of a strongly walk-regular digraph need not be diagonalizable, and secondly, the eigenvalues can be non-real. The concept of ...
The journal publishes papers in which combinatorics and algebra interact in a significant and interesting fashion. This interaction might occur through the study of combinatorial structures using algebraic methods, or the application of combinatorial methods to algebraic problems. Journal Of Algebraic Combin...
Given two finite-dimensional representations\pi _1 :G \rightarrow GL(W_1)and\pi _2 :G \rightarrow GL(W_2)of a groupG, we say that the representation\pi _1isimmersedin the representation\pi _2if the eigenvalues of\pi _1(g), counting multiplicities, are contained in the eigenvalues ...
Coverage Areas: Although the list is not prescriptive, Journal of Algebraic Statistics intends to focus on advances in the following sub-domains: Computational Theory Computer Science Ring and Module theory Group theory Semigroup theory Linear Algebra, Algebraic combinatorics Algebraic graph theory, Homo...
Coverage Areas: Although the list is not prescriptive, Journal of Algebraic Statistics intends to focus on advances in the following sub-domains: Computational Theory Computer Science Ring and Module theory Group theory Semigroup theory Linear Algebra, Algebraic combinatorics Algebraic graph theory, Homo...
More specifically, we show that if f is a vector valued harmonic Maass form of weight 1/2 whose principal part is defined over a number field K, and whose shadow lies in the space of unary theta functions, then all coefficients of the holomorphic part of f lie in K. This contrasts a...
We generalize the concept of partial permutations of Ivanov and Kerov and introduce k-partial permutations. This allows us to show that the structure coeff
on finite groups will be obtained as direct consequences. Finally, we will discuss some general methods of constructions of bent functions on group actions (see Theorems5.1and5.2in Sect.5). We will also construct some examples of bent functions on group actions (see Examples5.3and5.4in Sect.5...