Brualdi and Ma found a connection between involutions of length $n$ with $k$ descents and symmetric $k \times k$ 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.
Combinatorial proofs for identities related with generalizations of the mock theta functions $ω(q)$ and $ν(q)$
Combinatorial proof of identities involving partitions with distinct even parts and 4-regular partitions
Combinatorial proofs of some linear algebraic identities
![QR code for arXiv:1410.7356 [math.CO]](http://oss.arxitics.com/images/favicon.svg)