generating statistics for a partition

... Acta Math Sin., to appear [8] H.H Chan and P.C Toh, New analogues of Ramanujan’s partition idenities, J Number Theory, 130 (2010), 1898–1913 [9] B Kim, A crank analog on a certain kind of partition ... H.-C Chan, Ramanujan’s cubic continued fraction and Ramanujan type congruences for a ceratin partition function, Int J Number Theory, (2010), 819–834 [7] H.-C Chan, Distribution of a certain partition ... Spirit of Ramanujan, Amer Math Soc., Providence, 2006 [3] J.M Borwein, P.B Borwein and F.G Garvan, Some cubic modular identites of Ramanujan, Trans Amer Math Soc., 343 (1994), 35–47 [4] Z Cao, On...

Ngày tải lên: 08/08/2014, 14:22

... corollary is also immediate Corollary For all n ≥ 0, b(7n + a) ≡ (mod 7), if a = 2, 3, 4, or combinatorial interpretation of M ∗(m, n) To give a combinatorial explanation of the famous Ramanujan partition ... Kim, A crank analog on a certain kind of partition function arising from the cubic continued fraction, Acta Arith 148 (2011), 1–19 [7] H Zhao and Z Zhong, Ramanujan type congreuences for a certain ... function are known, it is natural to seek a partition statistic to give a combinatorial explanation of the known congruences In this paper, we will give two partition statistics for the cubic partitions...

Ngày tải lên: 08/08/2014, 14:23

... lead capture, coordinating email marketing campaigns, managing pay-per-click advertising programs and integrating all of these so that all leads are captured and scored in a consistent way A ... which tools are most effective at generating high quality leads Finally, this approach is easy to scale-up without having to increase headcount You can automate email follow-up campaigns, run ... Google pay-per-click ads and your website can capture visitor details 24 hours a day, days a week, all without intensive manual input Building a Demand Generation Machine Many B2B companies suffer...

Ngày tải lên: 30/03/2014, 12:20

... control-oriented functionality (an ARM for the signalling part and a StarCore for the multimedia part) It features several hardware accelerating units (ASICs), for the more data-oriented and computation intensive ... directed acyclic graph (DAG) The objective function incorporates several constraints on the available silicon area (hardware capacity), B Knerr et al memory (software capacity), and latency as a timing ... constraints like time, area, power, throughput, delay, and so forth Hardware then usually addresses the implementation of a functional part, for example, performing an FIR or CRC, as a dedicated hardware...

Ngày tải lên: 22/06/2014, 06:20

... Erd¨s and R Rado A partition calculus in set theory Bull Amer Math Soc., o 62:427–489, 1956 [4] Paul Erd˝s, Andr´s Hajnal, Attila M´t´, and Richard Rado Combinatorial set theo a ae ory: partition ... holds for o any two natural numbers m and n Fact (J Baumgartner A Hajnal) For any two natural numbers m and n, if Z is a real order, then Z → ((ω + m)n , ω)2 In each case a much stronger statement ... References [1] J Baumgartner and A Hajnal A proof (involving Martin’s axiom) of a partition relation Fund Math., 78(3):193–203, 1973 [2] James E Baumgartner A new class of order types Ann Math Logic,...

Ngày tải lên: 07/08/2014, 06:20

... of the tableau decreases by when the labels are decreased A tableau that has a label of lying above the can be transposed about the diagonal and this tableau is isomorphic to a tableau of content ... ωT is the tableau that is flipped about the diagonal Each standard tableau has either the label of lying to the immediate right of or above it A tableau that has a that lies immediately to the ... previous section The ’atoms’ of the Macdonald polynomials and the µ − type of the standard tableaux suggest that the tableaux naturally fall into standard tableaux classes a For a sequence s ∈ , ×...

Ngày tải lên: 07/08/2014, 06:22

... P has the same cardinality, that is |A| = c, for all A ∈ P If k does n not divide n, a partition P ∈ Pk is said to be almost uniform if every class A ∈ P has |A| = n/k or |A| = n/k n A partition ... The largest Sperner partition system in Pk is an almost-uniform partition system For the case where n = ck, where c and k are integers, an almost-uniform partition system is a uniform partition ... c-uniform Assume that |P| = k n Let A be the Sperner set system formed by taking c all classes from all the partitions in P, then |A| = n and c ≤ n c Since t (A) = A A |A| = c, from Kleitman and...

Ngày tải lên: 07/08/2014, 08:22

... Mukhin and Y Takeyama, Fermionic formulas for (k, 3)-admissible configurations, math.QA/0212347 [13] J.-F Fortin, P Jacob and P Mathieu, Jagged partitions, to appear in Ramanujan J., math.CO/0310079 ... overpartitions and jagged partitions and also for pointing out references [6] and [18] We also thank the referee for drawing our attention to lattice paths References [1] G.E Andrews, An analytic ... J.-F Fortin, P Jacob and P Mathieu, SM(2,4κ) fermionic characters and restricted jagged partitions, to appear in J Phys A: Math Gen 38 (2005), hep-th/0406194 [15] P Jacob and P Mathieu, Graded parafermions:...

Ngày tải lên: 07/08/2014, 08:22

... journal of combinatorics 12 (2005), #R30 c a c b a c b 24 23 19 a c b b a c a b 21 a b 12 a c b 17 b c a 25 a b c c c b b a b a 13 c a c c c 22 b 11 10 b a a c b b a a c c c 14 b c a b b a c b a ... an umbra A if eval(An ) = an for all n In practice, the word eval is usually dropped and we simply write An = an with the understanding that the functional has been applied When we write f (A) ... /2 n! n=0 All of our formulas for hn (u) are easily converted into formulas for Hn (u) Foata [5] gave a combinatorial proof of Doetsch’s identity [2] giving a generating function for h2n (u):...

Ngày tải lên: 07/08/2014, 13:21

... Acknowledgments The author thanks Herbert Wilf and Janet Beissinger, who was the first to explore [1] combinatorial proofs using colored permutations, for their assistance References [1] Janet Beissinger ... Colorful proofs of generating function identities Unpublished notes, 1981 [2] Richard P Stanley Enumerative combinatorics Vol 1, volume 49 of Cambridge Studies in Advanced Mathematics Cambridge University ... ˜ π ˜ Note that R(π,f ) = Rφ((π,f )) for all (π, f ) ∈ Sn ,A , and that therefore φ is involutive Note further that, if (π, f ) = φ((π, f )) = (˜ , f), κ(π) = κ(˜ ) ± Note finally that π ˜ π (π,...

Ngày tải lên: 08/08/2014, 01:20

... (1.2) A surprisingly large number of results on generating functions for various permutation statistics that have appeared in the literature as well as a large number of new generating functions for ... the remaining bricks, and the labels on cells and are x, the label on cell is 1, and the remaining labels are as before We can accomplish this by replacing hn in (5.5) by pu for an appropriate u ... )pu1 ha2 · · · hak instead of a sgn(T )ha1 ha2 · · · hak The authors would like to thank the anonymous referee for a very careful reading of the paper and suggestions that improved the presentation...

Ngày tải lên: 08/08/2014, 12:22

... time average and power of the signal x.t/ from Fig 1.3.1 Use a symbolic manipulation language such as Mathematica or Matlab if you like 1.5.12 Using a computing platform such as Mathematica, Maple, ... Signals Fig 1.1.8 A signal (again, an image) representing the large-scale and apparently random distribution of mass in the universe The data come from the APM galaxy survey and show more than ... curriculum is almost impossible A gaggle of graduate students in applied mathematics, statistics, and assorted engineering areas also regularly enrolls They are often asked to make in-class presentations...

Ngày tải lên: 05/09/2016, 23:35

Ngày tải lên: 08/08/2012, 17:20

Ngày tải lên: 04/10/2012, 10:02

... research funding, diarrhoea 60 million dollars in research funding, malaria 50 million dollars and TB 20 million dollars in research funding In conclusion it is clear that funding allocation for ... model answer: The graphs compare the number of deaths caused by six diseases in Someland in 1990 with the amount of research funding allocated to each of those diseases It can be clearly seen that ... deaths from leprosy, 0.3 million deaths from tropical diseases, 0.5 million deaths from diarrhoea, 0.4 million deaths from malaria and 1.8 million deaths from TB These figures can be contrasted...

Ngày tải lên: 04/10/2012, 10:02

... situation had changed radically by 1995 In 1995, 90% of women in Someland had completed secondary education and of those, half had graduated from an initial degree and 20% had gone on to postgraduate ... postgraduate studies At the other end of the scale we can see that by 1995 all girls were completing lower secondary, although 10% ended their schooling at this point This is in stark contrast with ... girls completed primary school, 35% had no schooling at all and 35% only completed the third grade In conclusion, we can see that in the 50 years from 1945 to 1995 there have been huge positive...

Ngày tải lên: 04/10/2012, 10:02

... Use a startup expenses and capitalization spreadsheet as a guide to preparing a balance sheet as of opening day Then detail how you calculated the account balances on your opening day balance ... and financial management A balance sheet shows what items of value are held by the company (assets), and what its debts are (liabilities) When liabilities are subtracted from assets, the remainder ... appear in the cash flow at all because you never write a check for it Opening Day Balance Sheet A balance sheet is one of the fundamental financial reports that any business needs for reporting and...

Ngày tải lên: 23/10/2012, 15:46

... principles and applications in aerospace medicine Aviat Space Environ Med 2007, 78:973-978 Thibeault C, Evans A; Air Transport Medicine Committee, Aerospace Medical Association: Emergency medical kit for ... Critical Care Vol 13 No Ruskin aerospace medical researchers, and the traveling public Sand and colleagues’ study should serve as a template for future research in this important area Competing ... kit for commercial airlines: an update Aviat Space Environ Med 2007, 78: 1170-1171 European Joint Aviation Authorities: JAR-OPS1, Commercial Air Transportation (Aeroplanes), Global Engineering...

Ngày tải lên: 25/10/2012, 10:06

... M, Hirai M, Tominaga N, Nakajima H, Elisseeva OA, Masuda T, Nakano A, Kawakami M, Oji Y, Ikegame K, Hosen N, Udaka K, Yasukawa M, Ogawa H, Kawase I, Sugiyama H: Wilms tumor gene peptide-based ... Ikegame K, Hosen N, Yoshihara S, Wu F, Fujiki F, Murakami M, Masuda T, Nishida S, Shirakata T, Nakatsuka S, Sasaki A, Udaka K, Dohy H, Aozasa K, Noguchi S, Kawase I, Sugiyama H: Induction of WT1 ... peptide vaccine and the resultant cancer regression Proc Natl Acad Sci U S A 2004;101:13885-13890 Kawakami M, Oka Y, Tsuboi A, Harada Y, Elisseeva OA, Furukawa Y, Tsukaguchi M, Shirakata T, Nishida...

Ngày tải lên: 26/10/2012, 09:39

... meetings and other necessary tasks that require a good deal of organization S/he will be dependable and will easily adapt to the ever-present changes that befall a department manager Click here for additional ... than enhance it Finding a person with a careful balance of Influence and Dominance is extremely important Click here for additional help with evaluating sales managers Page 17 Hiring… For A Pe ... www.xbcoaching.com Chapter Seven Hiring Department Managers That Are A Perfect Fit © Kathi Graham-Leviss http://www.xbcoaching.com Regardless of the particular area of the company, each department manager...

Ngày tải lên: 06/11/2012, 15:40