The spt-crank for overpartitions
WebAug 30, 2024 · In 1916, Ramanujan’s showed the spt-crank for marked overpartitions. The corresponding special functions S z, x , S1 z, x and S2 z, x are found in Ramanujan’s notebooks, part 111. In 2009, Bingmann, Lovejoy and Osburn defined the generating functions for spt n , spt n 1 and spt n 2 . In 2012, Andrews, Garvan, and Liang defined the … WebAug 13, 2024 · Monotonicity properties for ranks of overpartitions @article{Xiong2024MonotonicityPF, title={Monotonicity properties for ranks of overpartitions}, author={Huan Xiong and Wenston J. T. Zang}, journal={Journal of Number Theory}, year={2024} }
The spt-crank for overpartitions
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WebIntroductions → the crank of partition pairs λ = (λ1, λ2 ) and analyze the In this paper we give some related definitions of spt (n), Corollary 3 with the help of 42 marked overpartitions of 6. various product notations, vector partitions and S - partitions, M S (m, n) , M S (m, t , n) , marked partition and sptcrank for 2. WebNov 14, 2013 · The spt-crank for overpartitions. November 2013; Acta Arithmetica 166(2) DOI:10.4064 ... and Liang defined an spt-crank in terms of weighted vector partitions …
WebIn 1916, Ramanujan’s showed the spt-crank for marked overpartitions. The corresponding special functions S z,x , S 1 z,x and S 2 z,x are found in Ramanujan’s notebooks, part 111. WebTHE SPT-CRANK FOR OVERPARTITIONS FRANK G. GARVAN AND CHRIS JENNINGS-SHAFFER Abstract. Bringmann, Lovejoy, and Osburn [14, 15] showed that the generating functions of the spt-overpartition functions spt (n), spt1(n), spt2(n), and M2spt(n) are quasimock theta functions, and satisfy a number of simple Ramanujan-like congruences.
WebMay 20, 2024 · The spt-crank for overpartitions. Acta Arith. 166(2), 141–188 (2014) Article MathSciNet MATH Google Scholar Jennings-Shaffer, C.: Another SPT crank for the … WebFor all the overpartition functions except M2spt(n) we are able to define the spt-crank purely in terms of marked overpartitions. The proofs of the congruences depend on Bailey’s …
WebFor all the overpartition functions except M2spt(n) we are able to define the spt-crank purely in terms of marked overpartitions. The proofs of the congruences depend on Bailey's …
WebAug 30, 2024 · In 1916, Ramanujan’s showed the spt-crank for marked overpartitions. The corresponding special functions S z, x , S1 z, x and S2 z, x are found in Ramanujan’s … ruby carrWebAug 21, 2024 · The spt-crank for overpartitions. Acta Arith. 166(2), 141–188 (2014) Article MATH MathSciNet Google Scholar Jennings-Shaffer C.: Higher order SPT functions for overpartitions, overpartitions with smallest part even, and partitions with smallest part even and without repeated odd parts. J. Number Theory 149, 285–312 (2015) ... ruby carousel® barberryWebLet $${\overline{spt}}(n)$$ spt ¯ ( n ) denote the number of smallest parts in the overpartitions of n where the smallest part is not overlined. In recent years, some ... The definitions of the rank and crank for overpartitions were given by Bringmann, Lovejoy and Osburn. Let N¯(s,l;n)\documentclass[12pt]{minimal} \usepackage{amsmath ... scan file to network driveWebNov 20, 2014 · PDF In 2009, Bingmann, Lovejoy and Osburn defined the generating function for (spt) ̅(n). ... Crank, Non-Negative, Overpartitions, Overlined ... Again there ar e 6 marked over partitions of 3 ... scan files to pdf windows 10WebApr 1, 2024 · The spt-crank for overpartitions. Acta Arith., 166 (2) (2014), pp. 141-188. CrossRef View in Scopus Google Scholar [23] F. Garvan, D. Kim, D. Stanton. Cranks and t-cores. ... Higher order SPT functions for overpartitions, overpartitions with smallest part even, and partitions with smallest part even and without repeated odd parts. scan file using only scanner javaWebHigher Order Spt Functions for Overpartitions, Overpartitions With Smallest Part Even, ... 149:285-312. 2015-04-01. Another Spt Crank for the Number of Smallest Parts in Overpartitions With Even Smallest Part. Journal of Number Theory. 148:196-203. 2015-03-01. A Note On the Transcendence of ... ruby car reviewsWeboverpartitions of 5n 3 when n =1. Some related definitions In this section we have described some definitions related to the article following7. spt2 n 4: Th enu mb rof sal tp in the overpartitions of n with smallest part not overlined and even is denoted by spt2 n for example, n spt2(n) 1 : 0 2 : 2 1 3 : 0 ruby carrera