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Enumeration of pyramids of one-dimensional pieces of arbitrary fixed integer length

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  • 0902

    Submitted manuscript, 127 KB, PDF-document

We consider pyramids made of one-dimensional pieces of fixed integer length a and which may have pairwise overlaps of integer length from 1 to a. We prove that the number of pyramids of size m, i.e. consisting of m pieces, equals (am-1,m-1) for each a >= 2. This generalises a well known result for a = 2. A bijective correspondence between so-called right (or left) pyramids and a-ary trees is pointed out, and it is shown that asymptotically the average width of pyramids is proportional to the square root of the size.
Original languageEnglish
PublisherMuseum Tusculanum
StatePublished - 2009

Bibliographical note

Keywords: math.CO; 05A15; 82B41

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