Search Results - "algebraic combinatorics"

Further results on permanents of Laplacian matrices of trees by Wu Tingzeng, Dong Xiangshuai

“…The research on the permanents of graph matrices is one of the contemporary research topic in algebraic combinatorics. Brualdi and Goldwasser characterized the upper and lower bounds of permanents of Laplacian matrices of trees. …”
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Splines on Cayley graphs of the symmetric group by Nathan R. T. Lesnevich

“…These cohomology rings carry two actions of the symmetric group $S_n$ whose graded characters are both of general interest in algebraic combinatorics. In this paper, we generalize the graded $S_n$ -representations from the cohomologies of the above varieties to splines on Cayley graphs of $S_n$ and then (1) give explicit module and ring generators for whenever the $S_n$ -generating set is minimal, (2) give a combinatorial characterization of when graded pieces of one $S_n$ -representation is trivial, and (3) compute the first degree piece of both graded characters for all generating sets.…”
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