Báo cáo toán học: "On an identity for the cycle indices of rooted tree automorphism groups" doc
Báo cáo toán học: "On an identity for the cycle indices of rooted tree automorphism groups" doc
... related to the automorphism groups of
trees have been investigated. We state, for instance, the enumeration of identity trees
(see [7]), and the question of determining the average size of the automorphism ... to G. Labelle for the summed cycle indices
of all rooted trees, which resembles the well-known formula for the cycle index of
the symme...
Báo cáo toán học: "Conjectured Combinatorial Models for the Hilbert Series of Generalized Diagonal Harmonics Modules" docx
... partition of 31 having seven parts.
The transpose λ
of λ is the partition obtained by interchanging the rows and columns of
the Ferrers diagram of λ. For example, the transpose of the partition ... summation formula for their generating
function and giving bijective proofs of the equivalence of different pairs of statistics.
As before, these bijections imply...
Báo cáo toán hoc:"On Suborbital Graphs for the Normalizer of Γ0(N )" pot
... seen easily that the length of any circuit is an even number. Therefore we can give
the following corollary.
Corollary 3. Let N (Γ
0
(N)) act transitively on
ˆ
Q. Then the length of any circuit in
G(∞, ... (Γ
0
(m)). The following theorem shows that the same is true for the graph G(∞, 1).
Theorem 3.3. Let m be a square-free positive integer. If any circuit in the graph G...
Báo cáo toán học: "TIGHT UPPER BOUNDS FOR THE DOMINATION NUMBERS OF GRAPHS WITH GIVEN ORDER AND MINIMUM DEGREE" pdf
... B and there
must be at least 6 of the A
v
’s that have cardinality 2. If there were more than 6
the argument for case (1a) repeated would show the existence of a vertex of degree
greater than ... A
v
’s of
the form {x, z} and {y,w} or, of the form {x, w} and {y, z}. But this contradicts
our assumption that the two element A
v
’s are never disjoint. This completes the...
Báo cáo toán học: "Tight Upper Bounds for the Domination Numbers of Graphs with Given Order and Minimum Degree, II." pdf
... isomorphism of circulant graphs. For each
S ⊆{±1, ±2, ,±9} Fisher and Spaulding [5] obtained a formula for the domination
number of the circulant graph C(S, n) as a function of n and S, but results and ... filling another
missing entry in the table of values of γ(n, δ)in[2]
Acknowledgement We wish to thank Gordon Royle for providing Cayley tables for
the 14 groups of...
Báo cáo toán học: " Vizing-like conjecture for the upper domination of Cartesian products of graphs – the proof" pot
... note we prove the following conjecture of Nowakowski and Rall: For
arbitrary graphs G and H the upper domination number of the Cartesian prod-
uct G H is at least the product of their upper domination ... conjecture: For any graphs G and H, γ(G H) ≥ γ(G)γ(H),
where γ, as usual, denotes the domination number of a graph, and G H is the Cartesian
product of graphs...
Báo cáo toán học: "A recurrence relation for the “inv” analogue of q-Eulerian polynomials" ppsx
... where
des(σ) and inv(σ) denote, resp ectively, the descent number and inversion number
of σ in the symmetric group S
n
of degree n. We give an algebraic proof and a
combinatorial proof of the recurrence ... A recurrence relation for the “inv” analogue of
q-Eulerian polynomials
Chak-On Chow
Department of Mathematics and Information Technology,
Hong Kong Institute of Edu...
Báo cáo toán học: "A Combinatorial Formula for the Hilbert Series of bigraded Sn-modules" ppsx
... are the chosen numbers in the last line of the set and b(r
k
j
) is the number of
unchosen numbers which are bigger than r
k
j
(or, number of ◦’s to the right of r
k
j
). Full
explanation for the ... in the hook
shape case. This method is based on the combinatorial formula of Haglund , Haiman
and Loeh r for the Macdonald polynomials and extends the result of...
Báo cáo toán học: "Sharp lower bound for the total number of matchings of tricyclic graphs" doc
... orders, as well as for coding of chemical structures [12, 13, 26,
32]. Therefore, the ordering of molecular graphs in terms of their Hosoya indices is of
int erest in chemical thermodynamics. Let ... index of hexagonal spiders.
In light of the information available for the total number of matchings of trees, unicyclic
graphs, bicyclic graphs, it is natural to consi...
Báo cáo toán học: "A normalization formula for the Jack polynomials in superspace and an identity on partitions" pps
... be the number of cells (including the possible circle at
the end of the row) to the right of s. Let a lso ℓ
Λ
(s) be the number of cells (not including
the possible circle at the bottom of the ... that the L.H.S. does not depend on the b
i
’s while the R.H.S. does. The proof
we provide of this identity relies crucially on the identification of the...