Tag Archives: acyclic orientations

Equivalence relations, 2

I believe, and have said in earlier posts here and here on this blog, that the Equivalence Relation Theorem is the modern pons asinorum, the bridge which you must cross in order to become a mathematician: it is essential to … Continue reading

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Poly-Bernoulli numbers

With Celia Glass and Robert Schumacher, I recently found a combinatorial interpretation of the poly-Bernoulli numbers of negative order. Bernoulli numbers The classical Bernoulli numbers are defined by a recurrence which can be written symbolically as (B+1)n+1 = Bn+1. The interpretation is: … Continue reading

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Counting colourings of graphs

Every graph theorist knows that the colourings of a graph with a given number of colourings are counted by a certain polynomial, the chromatic polynomial of the graph. My purpose here is to point out that there is more to … Continue reading

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