WebCYLINDRIC PARTITIONS IRA M. GESSEL AND C. KRATTENTHALER ABSTRACT. A new object is introduced into the theory of partitions that gener-alizes plane partitions: … WebSep 12, 2008 · MacMahon's classic generating function of random plane partitions, which is related to Schur polynomials, was recently extended by Vuletic to a generating function of weighted plane partitions that is related to Hall-Littlewood polynomials, , and further to one related to Macdonald polynomials, .
Peaks of Cylindric Plane Partitions
WebAug 26, 2024 · Cylindric partition generating functions for any profile were shown by Borodin to equal infinite products, and “sum-sides” were then found by Corteel and Welsh … Webcylindric partitions, and skew double-shifted plane partitions—and state the product generating functions for these that follow from Han and Xiong’s work in [13]. In Sect. 3, we record our Corteel–Welsh-type recurrences for two variable generating functions. In Sect. 4, we use these recurrences to prove Theorems 1.1, 1.2 and 1.3; gagny athlétisme
NonEuclid: 10: Disk and Upper Half-Plane Models - University of …
WebCylindric partitions were introduced by Gessel and Krattenthaler in [4], as plane par-titions satisfying certain constraints between the entries of the first and the last row. A particularly interesting special case of them, called (0,1)-cylindric partitions in [4], is equivalent to semistandard cylindric tableaux, as defined by Postnikov in [9]. Webcover the usual definition of a reverse plane partition (see, for example [Ada08] for a nice review). If, in addition to this there are no inversions in the profile (see definition 2.1) then we have a regular plane partition. A “cube” of a cylindric plane partition is defined to be a “box” of one of the underlying integer partitions. Web;r(q) has emerged, based on cyclindric partitions. Cylin-dric partitions, rst introduced by Gessel and Krattenthaler in [25], are an a ne analogue of plane partitions. Using notation and terminology as de ned in Section 3, let GK c(q) be the size (or norm) generating function of cylindric partitions of rank rand pro le c= (c 0;:::;c r 1): GK c ... auhype