Báo cáo toán hoc:" Permutation Statistics and q-Fibonacci Numbers " doc
Báo cáo toán hoc:" Permutation Statistics and q-Fibonacci Numbers " doc
... counted by the Fibonacci numbers. These distribu-
tions will give us q-Fibonacci numbers which are related to the q-Fibonacci numbers of
Carlitz [2], Cigler [3, 4], and Goyt and Sagan [6].
Let the ... produced a class of q-Fibonacci numbers , which
they related to q-Fibonacci numbers studied by Carlitz and Cigler. In this paper we
will study the d istributions of some M...
Báo cáo toán học: " Permutation Patterns and Continued Fractions" pptx
... π
1
is a permutation of the set {n − k +1, ,n−1} ,and
2
is a permutation of the set
{1, ,n−k}. Furthermore, π
1
and π
2
are each (132)-avoiding. Conversely, if π
1
and π
2
are (132)-avoiding permutations ... B´ona, Permutations with one or two 132-subsequences. Discrete Math. 181
(1998), no. 1-3, 267–274.
[2] Aaron Robertson, Permutations containing and avoiding 123 and 132 patte...
Báo cáo toán học: "Permutation Separations and Complete Bipartite Factorisations of Kn,n" pot
... k.Ifn
3
=2andt
k
=5,thenwe
are covered by Sublemma 4.3.
If n
3
=1,n
2
≥ 2andt
k
≥ 6letu = 6and = (0 2)(1 4)(3 5) and apply Sublemma
4.1. If n
3
=1,n
2
= 1 or 2, and t
k
=5,letσ
k
= (0 3)(2 4)(1) and ... gives one permutation with separations u
u
0
1
.
As v ≥ 3, u ≥ 7andsou +4≤ 2(u − 1) and v +1<u− 2. Then Lemma 5 gives two
permutations with separations (u − 1)
u+4
and three gap...
Báo cáo toán học: "Permutation Tableaux and the Dashed Permutation Pattern 32–1" ppsx
... Babson and E. Steingr´ımsson, Generalized permutation patterns and a classifica-
tion of the Mahonian statistics, S´em. Lothar. Combin. 44 (2000), B44b.
[2] A. Burstein, On some properties of permutation ... #R108.
[6] S. Corteel and J. S. Kim, Combinatorics on permutation tableaux of type A and type
B, European J. Combin. 32 (2011), 563-579.
[7] S. Corteel and P. Nadea u, Bij...
Báo cáo toán học: "Aviezri Fraenkel and Combinatorial Games" doc
... integers, on the one hand, and Wythoff’s Game [9, 39, 11, 1, 8]
on the other. Wythoff’s Game is played with two heaps from which players alternately
take any number from one heap or equal numbers from each; ... [37],
Multivision [26], partizan octal and subtraction games [38] and extensions of Conway’s
‘short games’ [52].
He has been especially interested in annihilation games [10, 53,...
Báo cáo toán học: "MacWilliams identities and matroid polynomials" doc
... cases are similar, and R
g,h
satisfies conditions 1 and 2. The conditions
1, 2, and 3 recursively define R
g,h
, which proves the uniqueness of the function R
g,h
.
Suppose that g(x)andh(x) are functions ... that g(x),h(x) =0,andthat
f(M,x,y,{z
e
}
E
) is a function which satisfies conditions 2 and 3 for all M∈A.LetF
0
and F
1
denote the terms
f(U
0,1
,x,y,z
e
) − h(z
e
)
g(z
e
)
a...
Báo cáo toán học: "Spanning Trees and Function Classes" docx
... n.LetI
B
and I
S
be subsets of [k] and let B = {C
i
: i ∈ I
B
} and
S = {C
i
: i ∈ I
S
}. We refer to the sets B and S as the bases and summits of G
respectively. A set C
i
∈BiscalledabaseofG and ... line, and then we connect n to the lefthand
endpoint of the first cycle, the righthand endpoint of each cycle to the lefthand endpoint
of the cycle following it, and we connect the...
Báo cáo toán học: "BG-ranks and 2-cores" docx
... follows from Theorem 2 and item 4 above. ✷
Corollary 1 There exists a partition of n with BG-rank = j if and only if j + n is even
and j(2j − 1) ≤ n.
4 Congruences
Berkovich and Garvan’s motivation ... combinatorics 13 (2006), #N18 2
References
[1] Alexander Berkovich and Frank Garvan, On the Andrews-Stanley refinement of Ra-
manujan’s partition congruence modulo 5 and generalizati...
Báo cáo toán học: "Total domination and matching numbers in claw-free graphs" doc
... Factors and Factorization. 403–430. Handbook of Graph Theory ed. J.
L. Gross and J. Yellen. CRC Press, 2003, ISBN: 1-58488-092-2.
[11] W. R. Pulleyblank, Matchings and Extension. 179–232. Handbook ... journal of combinatorics 13 (2006), #R59 9
Total domination and matching numbers
in claw-free graphs
1
Michael A. Henning
∗
and
2
Anders Yeo
1
School of Mathematical Sciences
Univers...
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