“RAMANUJAN’S CONGRUENCES AND DYSON’S CRANK”
نویسندگان
چکیده
منابع مشابه
Ramanujan's congruences and Dyson's crank.
T he achievement of Karl Mahlburg in this issue of PNAS (1) adds a lustrous chapter to a unique mathematical object: the crank. In 1944, the crank was first hinted at by Freeman Dyson (2), then an undergraduate at Cambridge University. He had written an article, titled Some Guesses in the Theory of Partitions, for Eureka, the undergraduate mathematics journal of Cambridge. Dyson discovered the ...
متن کاملPartition congruences and the Andrews-Garvan-Dyson crank.
In 1944, Freeman Dyson conjectured the existence of a "crank" function for partitions that would provide a combinatorial proof of Ramanujan's congruence modulo 11. Forty years later, Andrews and Garvan successfully found such a function and proved the celebrated result that the crank simultaneously "explains" the three Ramanujan congruences modulo 5, 7, and 11. This note announces the proof of ...
متن کاملInfluence of crank length and crank-axle height on standing arm-crank (grinding) power.
OBJECTIVE To determine the optimal crank length and crank-axle height for maximum power production during standing arm cranking ("grinding"). METHODS Nine elite professional America's Cup grinders (age = 36 +/- 2 yr, body mass = 104 +/- 1 kg, body fat = 13% +/- 2%) performed eight maximal 6-s sprints on an adjustable standing arm-crank ergometer fitted with an SRM power crank. The protocol in...
متن کاملSOME INTUITIONISTIC FUZZY CONGRUENCES
First, we introduce the concept of intuitionistic fuzzy group congruenceand we obtain the characterizations of intuitionistic fuzzy group congruenceson an inverse semigroup and a T^{*}-pure semigroup, respectively. Also,we study some properties of intuitionistic fuzzy group congruence. Next, weintroduce the notion of intuitionistic fuzzy semilattice congruence and we givethe characterization of...
متن کاملDyson’s Crank Distribution Conjecture
Bringmann and Dousse recently established a conjecture of Dyson dealing with the limiting asymptotics of the Andrews-Garvan crank statistic for integer partitions. A direct “sieving” technique is used to establish this conjecture and establish the range of validity. Unlike the approach of Bringmann and Dousse, the technique readily yields the analogous result for Dyson’s partition rank and all ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Research -GRANTHAALAYAH
سال: 2014
ISSN: 2350-0530,2394-3629
DOI: 10.29121/granthaalayah.v2.i3.2014.3056