Selberg integrals, Askey–Wilson polynomials and lozenge tilings of a hexagon with a triangular hole
نویسندگان
چکیده
منابع مشابه
The Number of Centered Lozenge Tilings of a Symmetric Hexagon
Abstract. Propp conjectured [15] that the number of lozenge tilings of a semiregular hexagon of sides 2n − 1, 2n − 1 and 2n which contain the central unit rhombus is precisely one third of the total number of lozenge tilings. Motivated by this, we consider the more general situation of a semiregular hexagon of sides a, a and b. We prove explicit formulas for the number of lozenge tilings of the...
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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...
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Let a, b and c be positive integers and consider a hexagon with side lengths a,b,c,a,b,c whose angles are 120 (see Figure 1). The subject of our interest is lozenge tilings of such a hexagon using lozenges with all sides of length 1 and angles of 60 and 120. Figure 2 shows an example of a lozenge tiling of a hexagon with a = 3, b = 5 and c = 4. We introduce the following oblique angled coordina...
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15 صفحه اولDistances on Lozenge Tilings
In this paper, a structural property of the set of lozenge tilings of a 2n-gon is highlighted. We introduce a simple combinatorial value called Hamming-distance, which is a lower bound for the flipdistance (i.e. the number of necessary local transformations involving three lozenges) between two given tilings. It is here proven that, for n ≤ 4, the flip-distance between two tilings is equal to t...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2016
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2015.09.006