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

Research output: Working paper


  • 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
Publication statusPublished - 2009

Bibliographical note

Keywords: math.CO; 05A15; 82B41

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ID: 16094367