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      Lozenge tilings of hexagons with a vertical intrusion

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          Abstract

          Motivated by the conjecture posed by Fulmek and Krattenthaler, we provide product formulas for the number of lozenge tilings of a hexagon with a vertical intrusion. As a direct corollary, we obtain the product formula for the number of plane partitions fitting inside a box with a certain restriction. We also investigate the asymptotic behavior of the ratio between the number of lozenge tilings of a hexagon with a vertical intrusion and that of one without it.

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          Author and article information

          Journal
          03 April 2021
          Article
          2104.01515
          104812fb-104c-4f41-b378-f8c7014b8e5b

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          History
          Custom metadata
          05A15
          22 pages, 11 figures. Any comments would be appreciated
          math.CO

          Combinatorics
          Combinatorics

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