Báo cáo toán học: "The Number of Permutation Binomials Over F4p+1 where p and 4p + 1 are Primes" doc

... when p divides m − n, all permutation binomials occur in pairs over F 4p+ 1 where p and 4p +1 areprimes. Theorem 12 Let q = 4p + 1where p and q are primes. The following are paired permu- tation binomials ... 6 (3) If 3p& lt;m< 4p then (mod 4) m ≡ 1 m ≡ 2 m ≡ 3 m ≡ 4 p ≡ 1 2 (p − 1) + N 1 + N 2 2N 1 2 (p − 1) + N 1 +...

Ngày tải lên: 07/08/2014, 13:21

... that S r +1 n +1 (q) − q r +1 · S r +1 n (q) − (q n−r − q r ) · S r n (q)=0. (Sasha  ) 1 Department of Mathematics, Temple University, Philadelphia, PA 19 122, USA. [ekhad,zeilberg]@math.temple.edu, http://www.math.temple.edu/~[ekhad, ... coefficients are defined by  m n  q := (1 − q m ) (1 − q m 1 ) ··· (1 − q m−n +1 ) (1 − q) (1 − q 2 ) ··· (1 − q n ) , (Carl) when...

Ngày tải lên: 07/08/2014, 06:20

... 18 092368 423 918 432 2623622400 14 40950 20545920 11 19730032 15 1894 915 20 15 5 712 15 337560 2 014 030656 5 717 8432080 16 719 3760 2 516 883 516 14 848635 316 5 17 19 22760 218 16 610 20 2745 512 34345 18 223440 12 85377660 ... 10 0 720 360 8 45 2445 7560 2520 9 10 3525 46830 84000 2 016 0 10 2637 13 29 51 835800 997920 18 1440 11 11 25 210 8 61 3 915 240 14 75 712...

Ngày tải lên: 07/08/2014, 07:21

... 79 11 4, 19 94. [8] Merino, C.: Chip-firing and the Tutte polynomial. Annals of Combinatorics, 1, 253– 259, 19 97. [9] Plautz J. and Calderer, R.: G-parking functions and the Tutte polynomial. Preprint. [10 ] ... Theorem 1 follows by the previous result. A permutation σ ∈ S n is an up-down permutation if σ (1) < σ(2) > σ(3) < . . Let a n be the number of up-down...

Ngày tải lên: 07/08/2014, 15:22

... f [00] w (zf [00] w 1 + z 3/2 f [ 01] w 1 + z 3/2 f [10 ] w 1 + z 2 f [11 ] w 1 ) (16 ) f [ 01] w = f [00] w (z 1/ 2 f [00] w 1 + zf [ 01] w 1 ) (17 ) f [10 ] w = f [00] w (z 1/ 2 f [00] w 1 + zf [10 ] w 1 ) (18 ) f [11 ] w = ... z 2 j w 1 ) (46) g w AZ w = P w AZ w AZ w 1 (z 1/ 2 P w 1 + zh w 1 ) (47) h w AZ w = P w AZ w AZ w 1 (z 1/ 2...

Ngày tải lên: 07/08/2014, 15:22

... t) 256t 6 + (3t + 1) 2 ( 1 + t) 6 ln(2t + 1) 512 t 6 + (3t + 1) ( 1 + t) 3 ln(3t + 1) 32t 3 + (t − 1) 4 8388608t 4 (t + 3) (3t + 1) 5  19 683t 11 − 13 122t 10 19 0269t 9 + 12 2862096t 8 + 626 914 188t 7 + ... −2 + xz) 4x + (1 + z) log  1 + y 1 + z  − log (1 + z) 2 + log (1 +...

Ngày tải lên: 07/08/2014, 21:20

... d(n). where φ is the Euler function (see [I] and the references given there and exercise 7 .11 2 b in [St]). The number of planar trees with n + 1 nodes and the number of planar binary trees with n + ... Draw a punctured polygon with n the electronic journal of combinatorics 16 (2009), #R49 14 n d(n) 3 4 4 6 5 26 6 80 7 246 n d(n) 8 810 9 2704 10 9252 11 3206...

Ngày tải lên: 07/08/2014, 21:21

... 010 011 00 010 011 1 011 00 010 011 000 010 011 00 010 011 1 011 00 010 011 010 010 011 00 010 011 1 011 0 010 111 0 010 010 011 00 010 011 1 011 0 010 111 0 011 010 011 1 011 00 010 011 010 0 011 0 010 010 011 1 011 00 010 011 010 0 011 0 011 30 010 011 00 010 011 1 011 00 010 011 00 01 010 011 00 010 011 1 011 00 010 011 010 0 010 011 00 010 011 1 011 0 010 111 0 011 0 31 ......

Ngày tải lên: 08/08/2014, 12:23

... vertex u 1 of copy i + 1 ( for 1 ≤ i ≤ t − 1) . Let P ⊂ W t be the path in W t connecting the first copy of u 1 to the last copy of u l +1 , and number its vertices by 1, . . . , lt + 1 in the natural ... numbers of graphs. The Fibonacci Quarterly, 20 (1) :16 – 21, 19 82. [13 ] A. Scott and A. Tateno. On the number of t riang les and other complete...

Ngày tải lên: 08/08/2014, 12:23

... formula,  l≤w 1  jw l +1  = O (1)  jw w  = O((ej) w ). Since  l≤w 1 (q − 1) l n 1  i=jw  i l  =  l≤w 1 (q 1) l  n l +1  −  jw l +1  =(q 1) w 1  n w   1+ O(w/n)  + O((ejq) w ) = (q − 1) w 1 n w w!  1+ O(w 2 /n)  + ... ···(q d −q i(w 1) +w−2 ) × (q − 1) w 1 ways and so N a =  q d (q − 1)  j(w 1) j(w 1) 1  t=0 (1 − q t−d ) = ...

Ngày tải lên: 07/08/2014, 06:20