Báo cáo toán học: " A Bijective Proof of Garsia’s q-Lagrange Inversion Theorem" pdf
Báo cáo toán học: " A Bijective Proof of Garsia’s q-Lagrange Inversion Theorem" pdf
... Zeilberger
gave an alternative, much shorter proof of these identities in [5]. Zeilberger
gave a q-Foata proof of the q-Pfaff-Saalsch¨utz identity [20], inspired by Foata’s
bijective proof of the Pfaff-Saalsch¨utz ... q-Lagrange inversion
theorems of Garsia [7] and Garsia-Remmel [9]. Garsia, Gessel and Stanton, and
Singer have shown that Rogers-Ramanujan type identities ma...
Báo cáo toán học: "A Bijective Proof of Borchardt’s Identity" docx
... cells labelled by red
numbers and blue numbers. A cell may have no label, a red label, a blue label, or one
of each. At least one cell must have only one label. There is exactly one red label and
exactly ... and making the
substitutions γ(j)=i and γ(i)=j we obtain
a
i
− a
γ(i)
= a
γ(j)
− a
j
.
Since i ∈ A( z)andj ∈ A( z), the left hand side of this equation is ≥ 0andtherigh...
Báo cáo toán học: "A Bijective Proof of a Major Index Theorem of Garsia and Gessel" doc
... π) of shuffles of θ and π
and the set P(b, a) of partitions containing a parts (some of which may be zero) a ll less
than or equal to b. Both of these sets have cardinality
a+ b
a
=
n
a
. ... Classification: 0 5A0 5
Abstract
In this paper we provide a bijective proof of a theorem of Garsia and Gessel
describing the generating function of the major index...
Báo cáo toán học: "A combinatorial proof of Postnikov’s identity and a generalized enumeration of labeled trees" pdf
... electronic journal of combinatorics 11(2) (2005), #N3 3
A combinatorial pro of of Postnikov’s identity and
a generalized enumeration of labeled trees
Seunghyun Seo
∗
Department of Mathematics
Brandeis ... ,thelabelω(v)ofv should be
the smallest among the labels of the descendants of v. If we pick a labeling ω uniformly
at random, the probability that ω(v) is the smallest amo...
Báo cáo toán học: "A Short Proof of the Rook Reciprocity" pps
... Accepted: March 4, 1996.
Abstract. Rook numbers of complementary boards are related by a reciprocity
law. A complicated formula for this law has been known for about fifty years,
but recently Gessel and ... r
B
k
of a board are the number of subsets of B of size k such that no two elements
have the same first coordinate or the same second coordinate (i.e., the number of ways...
Báo cáo toán học: "A short proof of a partition relation for triples" pdf
... {i}.(Ingeneral,
if f is a function and A is a set, then by f A we mean the image of A under f.That
is, f A = {f (a) | a ∈ A} .) The failure of a partition relation is indicated by replacing
the ... be), if an order does not have countable
character, then it must have uncountable character.
1
We remark that an order X has
countable character if and only if the negative parti...
Báo cáo toán học: "A Concise Proof of the Littlewood-Richardson Rule" pdf
... representations of the q-
analogue of classical Lie algebras, J. Algebra 165 (1994), 295–345.
[L] P. Littelmann, A Littlewood-Richardson rule for symmetrizable Kac-Moody alge-
bras, Invent. Math. ... Combinatorial models for Weyl characters, Advances in Math.,
to appear.
[vL] M. A. A. van Leeuwen, The Littlewood-Richardson rule, and related combinatorics,
in “Interactions of Combina...
Báo cáo toán học: "A Combinatorial Proof of the Sum of q-Cubes" pptx
... note that the three subcases in 1 (a) are disjoint. Certainly case (i) as well as cases
(ii) and (iii) are disjoint as case (i) maps (λ, µ) to a 3-tuple with a primed third entry.
Cases (ii) and ... investigate other q-analogues of the sum of cubes formula. In addition, as
there are classical results for sums of other powers of integers, it would be natural to
develop q-analogues...
Báo cáo toán học: "A positive proof of the Littlewood-Richardson rule using the octahedron recurrence" pot
... with a bit of algebra, to the assumption that λ was
weakly decreasing.
This proposition can instead be proved by noting that adding an linear function of
y and z to a hive produces a new hive, and ... Then a is convex, i.e. a
i
≥
1
2
(a
i−1
+ a
i+1
). Put another way, the list (a
1
−
a
0
,a
2
− a
1
, ,a
n
− a
n−1
) is a weakly decreasing list of integers.
Proo...
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