347 research outputs found

    The Knowlton-Graham partition problem

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    A set partition technique that is useful for identifying wires in cables can be recast in the language of 0--1 matrices, thereby resolving an open problem stated by R.~L. Graham in Volume 1 of this journal. The proof involves a construction of 0--1 matrices having row and column sums without gaps

    A note on digitized angles

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    We study the configurations of pixels that occur when two digitized straight lines meet each other

    Overlapping Pfaffians

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    A combinatorial construction proves an identity for the product of the Pfaffian of a skew-symmetric matrix by the Pfaffian of one of its submatrices. Several applications of this identity are followed by a brief history of Pfaffians