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Bergfinnur Durhuus ; Søren Eilers - Combinatorial aspects of pyramids of one-dimensional pieces of fixed integer length

dmtcs:2794 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10) - https://doi.org/10.46298/dmtcs.2794
Combinatorial aspects of pyramids of one-dimensional pieces of fixed integer lengthConference paper

Authors: Bergfinnur Durhuus 1; Søren Eilers 1

  • 1 Department of Mathematical Sciences [Copenhagen]

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 give a combinatorial proof that the number of pyramids of size m, i.e., consisting of m pieces, equals \binom{am-1}{m-1} for each a \geq 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 equals \sqrt{\frac{\pi}{2} a(a-1)m}.


Volume: DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10)
Section: Proceedings
Published on: January 1, 2010
Imported on: January 31, 2017
Keywords: heaps,pyramids,polyominoes,lattice animals,enumeration,trees,Dyck paths,LEGOs,[INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS],[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM],[INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG]

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