
Recent Posts
Archives
 July 2016
 June 2016
 May 2016
 March 2015
 February 2015
 January 2015
 December 2014
 December 2013
 November 2013
 July 2013
 June 2013
 May 2013
 March 2013
 February 2013
 January 2013
 December 2012
 November 2012
 October 2012
 September 2012
 August 2012
 April 2012
 March 2012
 February 2012
 January 2012
 December 2011
 November 2011
 October 2011
Categories
Meta
Pages
Tag Archives: determinants
Polynomials and Representations XXXIX
Some Invariant Theory We continue the previous discussion. Recall that for we have a equivariant map which induces an isomorphism between the unique copies of in both spaces. The kernel Q of this map is spanned by for various fillings T with shape and entries … Continue reading
Polynomials and Representations XXXVIII
Determinant Modules We will describe another construction for the Schur module. Introduce variables for . For each sequence we define the following polynomials in : Now given a filling T of shape λ, we define: where is the sequence of entries from the … Continue reading
Polynomials and Representations XII
Lindström–Gessel–Viennot Lemma Let us switch gears and describe a beautiful combinatorial result. Suppose is a graph which is directed, has no cycles, and there are only finitely many paths from a vertex to another. Given sets of n vertices: the lemma … Continue reading
Polynomials and Representations XI
Here, we will give a different interpretation of the Schur polynomial, however this definition only makes sense in the ring For a given vector of nonnegative integers, define the following determinant, a polynomial in : For the case where , we … Continue reading
Posted in Uncategorized
Tagged determinants, partitions, pieri's formula, schur polynomials, young tableaux
Leave a comment
Introduction to Ring Theory (8)
Matrix Rings In this post, we’ll be entering the matrix. Let R be a ring. The ring Mn×n(R) is the set of matrices whose entries are elements of R, where the addition and multiplication operations are given by the usual matrix addition … Continue reading
Posted in Notes
Tagged advanced, cramer's rule, determinants, matrix rings, ring theory, rings, simple rings
Leave a comment