Another short proof of the Joni-Rota-Godsil integral formula for counting bipartite matchings
نویسندگان
چکیده
How many perfect matchings are contained in a given bipartite graph? An exercise in Godsil’s 1993 Algebraic Combinatorics solicits proof that this question’s answer is an integral involving a certain rook polynomial. Though not widely known, this result appears implicitly in Riordan’s 1958 An Introduction to Combinatorial Analysis. It was stated more explicitly and proved independently by S.A. Joni and G.-C. Rota [JCTA 29 (1980), 59–73] and C.D. Godsil [Combinatorica 1 (1981), 257–262]. Another generation later, perhaps it’s time both to revisit the theorem and to broaden the formula’s reach.
منابع مشابه
The algebra of set functions II: An enumerative analogue of Hall's theorem for bipartite graphs
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ورودعنوان ژورنال:
- Contributions to Discrete Mathematics
دوره 4 شماره
صفحات -
تاریخ انتشار 2009