Enumeration of Lozenge Tilings of Hexagons with a Central Triangular Hole
نویسندگان
چکیده
منابع مشابه
Enumeration of Lozenge Tilings of Hexagons with a Central Triangular Hole
We deal with the unweighted and weighted enumerations of lozenge tilings of a hexagon with side lengths a; b + m; c; a + m; b; c + m, where an equilateral triangle of side length m has been removed from the center. We give closed formulas for the plain enumeration and for a certain (?1)-enumeration of these lozenge tilings. In the case that a = b = c, we also provide closed formulas for certain...
متن کاملEnumeration of Lozenge Tilings of Punctured Hexagons
We present a combinatorial solution to the problem of determining the number of lozenge tilings of a hexagon with sides a, b + 1, b, a + 1, b, b + 1, with the central unit triangle removed. For a = b, this settles an open problem posed by Propp 7]. Let a, b, c be positive integers, and denote by H the hexagon whose side-lengths are (in cyclic order) a, b, c, a, b, c and all whose angles have 12...
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Abstract. Motivated by the enumeration of a class of plane partitions studied by Proctor and by considerations about symmetry classes of plane partitions, we consider the problem of enumerating lozenge tilings of a hexagon with “maximal staircases” removed from some of its vertices. The case of one vertex corresponds to Proctor’s problem. For two vertices there are several cases to consider, an...
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We generalize a special case of a theorem of Proctor on the enumeration of lozenge tilings of a hexagon with a maximal staircase removed, using Kuo’s graphical condensation method. Additionally, we prove a formula for a weighted version of the given region. The result also extends work of Ciucu and Fischer. By applying the factorization theorem of Ciucu, we are also able to generalize a special...
متن کاملEnumeration of Tilings of Diamonds and Hexagons with Defects
We show how to count tilings of Aztec diamonds and hexagons with defects using determinants. In several cases these determinants can be evaluated in closed form. In particular, we obtain solutions to open problems 1, 2, and 10 in James Propp’s list of problems on enumeration of matchings [22].
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2001
ISSN: 0097-3165
DOI: 10.1006/jcta.2000.3165