Báo cáo toán học: "Partition Identities I Sandwich Theorems and Logical 0–1 Laws" pps

... f(n) the electronic journal of combinatorics 11 (2004), #R49 14 Partition Identities I Sandwich Theorems and Logical 0–1 Laws Jason P. Bell Mathematics Department University of Michigan, East Hall, 525 ... possibly with different powers of x involved, then the resulting partition function is asymptotic to a positive constant times the original partition function. But first some de...

Ngày tải lên: 07/08/2014, 08:20

... q -Identities related to overpartitions and divisor functions Amy M. Fu Center for Combinatorics, LPMC Nankai University, Tianjin 300071, P.R. China Email: fmu@eyou.com Alain Lascoux Nankai University, ... Introduction In this paper, for any pair positive integers m, n, we prove the following two identities: n  i= 1  n i  (−1) i 1 (x +1)···(x + q i 1 ) (1 − q i ) m q mi = n ...

Ngày tải lên: 07/08/2014, 13:21

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Ngày tải lên: 05/08/2014, 09:46

... a i = i, b i = i, d i =0. G =    a i b i b i i i j 0 d j    →    b i a i a i i i j 0 d j    = G  . COMBINATORIAL PROOFS OF CAPELLI’S AND TURNBULL’S IDENTITIES FROM CLASSICAL ... imply, and were inspired by, identities of Cayley (see [T1]), Garding [G], and Shimura [S], respectively. In this paper, we give short combinatorial proofs of Capelli’...

Ngày tải lên: 07/08/2014, 06:20

... determinant identity, which is related to the afore- mentioned determinant identities. This is the subject of Section 5. It generalizes a determinant identity of Andrews and Burge [2]. Finally, in Section ... our determinant identities of Sections 4 and 5 into constant term identities which seem to be new. Auxiliary results that are needed in the proofs of our Theorems are collecte...

Ngày tải lên: 07/08/2014, 06:20

... known combinatorial identities including the orthogonality relations for Kravtchouk and Jacobi polynomials. This leads us to believe that these identities are novel. More important is, however, ... encountered in this paper is a rapidly developing subject, and it can be expected that finding identities like (2), (7) and (8) will shortly be a matter of computer power. Numerical simu...

Ngày tải lên: 07/08/2014, 06:23

... (Hamming) weight distri- butions (effective length distributions in Simonis’ terminology), and Shiromoto [11] on λ-ply weight enumerators. Section 2 of this paper introduces notation and the various enumerators, ... electronic journal of combinatorics 9 (2002), #R19 15 MacWilliams identities and matroid polynomials Thomas Britz Department of Mathematical Sciences, University of Aarhus,...

Ngày tải lên: 07/08/2014, 06:23

... size of a class in each partition. Then, |P| ≤ U(n−c, k −1). Moreover, this bound is tight if and only if P is a trivially 1-intersecting uniform partition system. Our second theorem deals with ... this proof applies to all c,itispresentedin this generality in Section 3. In Section 4, we mention a generalization of the concepts and results for when c does not divide n, which naturally ari...

Ngày tải lên: 07/08/2014, 13:21

... Rogers-Ramanujan identities and of identities of similar type, Electron. J. Combin. 1 (1994), R#10. [29] H. Rosengren and M. Schlosser, Elliptic determinant evaluations and the Macdonald identities for ... q 10  ∞ +∞  i= −∞ (−1) i q 5i 2 i x 5i+ 1 y 2i −  q 8 y; q 10  ∞ +∞  i= −∞ (−1) i q 5i 2 +i x 5i+ 2 y 2i+ 1 +  q 4 y; q 10  ∞ +∞  i= −∞ (−1) i q 5...

Ngày tải lên: 07/08/2014, 13:21

... η l η j =  i, k (η i M ij η k M kl + η k M kl η i M ij ) =  i, k η i η k [M ij , M kl ] (2.14) since η k η i = −η i η k . For i = k , the two terms in η i η k = −η k η i cancel if and only if [M ij , ... (2.15) which vanishes if and only if [M ij , M kj ] = 0 for all i, k. ✷ Some historical remarks. 1. Row-commutativity has arisen in some previous wor k on noncommu...

Ngày tải lên: 08/08/2014, 01:20