Partitions and Generating FunctionsHere we shall be concerned with manipulating objects built up from rows of squares as in Figure 2.1.Fig. 2.1Rows of squares. Rows of squares.doi:10.1007/978-3-030-71250-1_2mer EecioluAdriano M. Garsia
Using generating functions, Andrews proved that the number of partitions of n with initial B Darlison Nyirenda darlison.nyirenda@wits.ac.za Beaullah Mugwangwavari 712040@students.wits.ac.za 1 The John Knopfmacher Centre for Applicable Analysis and Number Theory, University of the Witwatersrand, 1 ...
M. Haiman, Notes on partitions and their generating functions, 2010. Google Scholar [8] B. Jayaram, S. Arumugam, K. Thulasiraman Dominator sequences in bipartite graphs Theoret. Comput. Sci., 694 (2017), pp. 34-41 View PDFView articleView in ScopusGoogle Scholar [9] S. Kitaev, S....
One of the results is a simple proof of MacMahon's [12] generating function for plane partitions. Previous results of this type [12, 4, 3, 8, 7] involved complicated algebraic methods which did not reveal any intrinsic “reason” why the corresponding generating functions have such a ...
Integer Partitions 作者:George E. Andrews/Kimmo Eriksson 出版社:Cambridge University Press 出版年:2004-10-11 页数:152 定价:USD 30.99 装帧:Paperback ISBN:9780521600903 豆瓣评分 评价人数不足 评价: 写笔记 写书评 加入购书单 分享到 推荐 当前版本有售· ··· 京东...
The treatment of IPs with generating functions and analytic combinatorics has been particularly impactful with regard to this question and we refer the interested reader to the comprehensive treatise given in [75]. Some constraints on IPs can also be taken into account with generating functions and ...
Explicit formulas for the associated exponential generating functions and for the totals of the respective statistics over all members of P(n,k) are found. To establish several of our results, we solve explicitly various linear partial differential equations. Finally, some comparable results are ...
partitions with odd parts and partitions with distinct parts. This is followed by chapters titled: Ferrers Graphs, The Rogers-Ramanujan Identities, Generating Functions, Formulas for Partition Functions, Gaussian Polynomials, Durfee Squares, Euler Refined, Plane Partitions, Growing Ferrers Boards, and ...
In a recent paper, the author generalised the first of these theorems to overparti- tions, using a new technique which consists in going back and forth between q- difference equations on generating functions and recurrence equations on their coefficients. Here, using a similar method, we ...
Statistics on permutations and rearrangements are defined and relationships between q -analogues of n , \\(n!\\) , and \\(\\binom{n}{k}\\) are proved. Integer partitions are defined and a few results concerning them are discussed. Generating functions are introduced as both elements of ...