Factored matrices can generate combinatorial identities
نویسندگان
چکیده
منابع مشابه
Combinatorial Proofs of Identities Involving Symmetric Matrices
Brualdi and Ma found a connection between involutions of length n with k descents and symmetric k×k matrices with non-negative integer entries summing to n and having no row or column of zeros. From their main theorem they derived two alternating sums by algebraic means and asked for combinatorial proofs. The purpose of this note is to give such demonstrations.
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let $a = (a_{i,j})_{1 leq i,j leq n}$ be an $n times n$ matrixwhere $n geq 2$. let $dt(a)$, its second immanant be the immanant corresponding to the partition $lambda_2 = 2,1^{n-2}$. let $g$ be a connected graph with blocks $b_1, b_2, ldots b_p$ and with$q$-exponential distance matrix $ed_g$. we given an explicitformula for $dt(ed_g)$ which shows that $dt(ed_g)$ is independent of the manner in ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2013
ISSN: 0024-3795
DOI: 10.1016/j.laa.2011.08.030