Counting Fiedler pencils with repetitions
نویسندگان
چکیده
We introduce a new notation based on diagrams to deal with Fiedler pencils with repetitions (FPR), and use it to solve several counting problems. In particular, we give explicit recurrences to count the number of FPRs of a given degree d, the number of symmetric, palindromic and antipalindromic ones (where the latter two structures are intended in the sense of [5]). We relate these structures to the presence of symmetries in the associated diagrams. Keyword: Matrix polynomials, linearizations, Fiedler pencils with repetitions MSC 2010: 65F15, 15A18, 15A22
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