Plane Partitions and Their Pedestal Polynomials
نویسندگان
چکیده
منابع مشابه
Polynomials associated with Partitions: Their Asymptotics and Zeros
Let pn be the number of partitions of an integer n. For each of the partition statistics of counting their parts, ranks, or cranks, there is a natural family of integer polynomials. We investigate their asymptotics and the limiting behavior of their zeros as sets and densities.
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Using the powerful machinery available for reduced words of type B, we demonstrate a bijection between centrally symmetric k-triangulations of a 2(n + k)-gon and plane partitions of height at most k in a square of size n. This bijection can be viewed as the type B analogue of a bijection for k-triangulations due to L. Serrano and C. Stump. Résumé. En utilisant la machinerie puissante pour mots ...
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The paper deals with a 3-parameter family of probability measures on the set of partitions, called the z-measures. The z-measures first emerged in connection with the problem of harmonic analysis on the infinite symmetric group. They are a special and distinguished case of Okounkov’s Schur measures. It is known that any Schur measure determines a determinantal point process on the 1-dimensional...
متن کاملReduced Words and Plane Partitions
Let w0 be the element of maximal length in the symmetric group Sn , and let Red(w0) be the set of all reduced words for w0. We prove the identity ∑ (a1,a2,...)∈Red(w0) (x + a1)(x + a2) · · · = ( n 2 ) ! ∏ 1≤i< j≤n 2x + i + j − 1 i + j − 1 , (∗) which generalizes Stanley’s [20] formula for the cardinality of Red(w0), and Macdonald’s [11] formula ∑ a1a2 · · · = ( 2 )!. Our approach uses an observ...
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ژورنال
عنوان ژورنال: Mathematical Notes
سال: 2018
ISSN: 0001-4346,1573-8876
DOI: 10.1134/s0001434618050115