Báo cáo toán học: "Franklin’s argument proves an identity of Zagier" pdf
Báo cáo toán học: "Franklin’s argument proves an identity of Zagier" pdf
... which,
miraculously, Franklin’s argument proves at once.
The author wishes to thank George Andrews and Don Zagier for supplying him with
copies of [3] and [8], and also an anonymous referee for ... [1] and
presented in more detail in [8]. Zagier [8] deduces (2) from (8), essentially by carefully
differentiating with respect to x and setting x =1.
Franklin’s argument proves an id...
Báo cáo toán học: "MacMahon’s theorem for a set of permutations with given descent indices and right-maximal record" ppt
... rev(r[max, v](σ)).
Proof. Let m = majcode(σ) and
r[max, v](σ) = r
1
. . . r
k
.
Recall that
1 r
1
< r
2
< · · · < r
k
= n
and r
i
is gr eater than any element of σ on the right of r
i
.
Let ... 17.
[10] P.A. MacMahon, The indices of permutations and derivation therefrom of functions
of a single variable associated wi th the permutations of any assemb l age of objects,...
Báo cáo toán học: "A note on the edge-connectivity of cages" pdf
... edge-connectivity of cages
Ping Wang
1∗
Baoguang Xu
2
Jianfang Wang
2
1
Department of Mathematics, Statistics and Computer Science,
St.Francis Xavier University, Antigonish, NS, Canada, B2G 2W5,
2
Institute of ... smaller cycle of G
to denote any cycle of G
having length less
than g.
∗
Research supported by the Natural Sciences and Engineering Research Council of Canada
the el...
Báo cáo toán học: "Nowhere-zero 3-flows in squares of graphs" pdf
... e
x
and e
y
, joining x and y
, y and x
, respectively.
Definition 2.2 Let G be a graph, let (D, f) be a 3-flow of G and let F ⊆ E(G)\supp(f).
A3-flow(D
,f
) of G is called an (F, f)-changer ... 3-flow of G and H be a subgraph of G
(1). If H
∼
=
W
4
and e ∈ E(H) \ supp(f) is a center edge, then an ({ e},f)-changer
exists.
(2). If H is a circuit of length 3 with E(H) ∩ supp(f...
Báo cáo toán học: "RAMANUJAN’S METHOD IN q-SERIES CONGRUENCES" potx
... For any prime p ≡ 5 or 11 (mod 12), the coefficient of q
pn−(p+1)/2
in
1
(q)
p−4
∞
∞
n=0
2n
n
q
n
5
3. Modular Forms.
Ramanujan, Ewell, Gandhi (and probably many others) have proved instances
of ... =7,a=b=1,c
7
(1, 1) = 2,α
m
=1ifm≥0, and 0 if
m<0, we see that
V
7m+5
≡ 0(mod7).
4
RAMANUJAN’S METHOD IN q-SERIES CONGRUENCES
by
George E. Andrews
(1)
and Ranjan Roy
Written in honor o...
Báo cáo toán học: "Escher''''s Combinatorial Patterns" pot
... tilings of
the plane by triangles and create patterns by decorating the triangles, but these were not
equilateral triangles. His focus of that investigation was not patterns, but rather the number of
different ... rotations of the translation
block. Case
Ca
consists of all signatures that use aspects 1, 2, and 3, case
Cb
consists of those
that use aspects 2, 3, and 4, and for...
Báo cáo toán học: "Dodgson’s Determinant-Evaluation Rule Proved by" pptx
... members of C(n) and those of B(n), such
that weight(S([π, σ])) = −weight([π, σ]). Hence the weights of the bad members of B(n) and C(n)
cancel each other in pairs, contributing a total of zero ... and σ is a matching of {2, . . . , n} to {2
, . . . , n
},
and define the weight similarly.
Let C(n) be the set of pairs [π, σ], where now n and 1
are unmarried and 1 and n
don’...
Báo cáo toán học: "Dumont’s statistic on words" pptx
... Frankl, and R. Stanley, The number of faces of balanced
Cohen-Macaulay complexes and a generalized Macaulay theorem, Combinatorica, 7
(1987), pp. 23–34.
[4] A. Bj
¨
orner, A. Garsia, and R. Stanley, ... to
an improved proof of Proposition 2.3.
the electronic journal of combinatorics 8 (2001), #R11 18
Dumont’s statistic on words
Mark Skandera
Department of Mathematics
University o...