Báo cáo toán học: "A Bijective Proof of Borchardt’s Identity" docx
Báo cáo toán học: "A Short Proof of the Rook Reciprocity" pps
... second coordinate (i.e., the number of ways of
“placing k non-taking rooks on B”). It has long been known [5] that the rook numbers
of a board B determine the rook numbers of the complementary board ... subset of [d] ì [d](where[d]isdenedtobe{1, 2, ,d})andtherook
numbers r
B
k
of a board are the number of subsets of B of size k such that no two elements
have t...
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...
Báo cáo toán học: " A Bijective Proof of Garsia’s q-Lagrange Inversion Theorem" pdf
... the q-Lagrange inversion
theorems of Garsia [7] and Garsia-Remmel [9]. Garsia, Gessel and Stanton, and
Singer have shown that Rogers-Ramanujan type identities may be derived by
means of q-Lagrange ... and Zeilberger
gave an alternative, much shorter proof of these identities in [5]. Zeilberger
gave a q-Foata proof of the q-Pfa-Saalschăutz identity [20], inspired by Foatas...
Báo cáo toán học: "A Concise Proof of the Littlewood-Richardson Rule" pdf
... extension of the Littlewood-Richardson rule [Z].
Taking the specialization λ =
, we obtain the decomposition of s
à/
into Schur
functions; it is simpler than the traditional formulation of the Littlewood-Richardson
rule ... the same tableaux.
Via the specialization ν =
, we obtain yet another formulation of the Littlewood-
Richardson rule in this case involving th...
Báo cáo toán học: "A Combinatorial Proof of the Sum of q-Cubes" pptx
... number of boxes in the first row is equal to the
size of the first part, the number of boxes in the second row is equal to the size of the
second part, etc. For example, the Ferrers diagram for the ... introduction to the basics of
partition theory, see [1].
2 q-analogue of the Sum of Cubes
In this section we introduce the following polynomial generalizat...
Báo cáo toán học: "A Bijective Proof of Borchardt’s Identity" docx
... present a bijective proof of Borchardt’s identity, one which relies only
on rearranging terms in a sum by means of sign-reversing involutions. The proof reveals
interesting properties of pairs of permutations. ... sign-reversing involution of C(p, q).
Theorem 3.8 implies that equation (2.3) is true, hence we have a bijective proof of
Borchardt’s identity.
the electro...
Báo cáo toán học: "A positive proof of the Littlewood-Richardson rule using the octahedron recurrence" pot
... an octahedron, though, one of the old vertices (a local height max)
the electronic journal of combinatorics 11 (2004), #R61 9
A positive proof of the Littlewood-Richardson rule
using the octahedron ... give a bijective proof of this, using the octahedron rule
from [RR, P, FZ, S]. This bijection was first found by CW in the honeycomb model,
where the...
Báo cáo toán học: "A Combinatorial Proof of the Log-concavity of a famous sequence counting permutations" potx
... Subject Classifications: 0 5A0 5, 0 5A1 5
To Richard Stanley, who introduced me to the area of log-concave sequences.
Abstract
We provide a combinatorial proof for the fact that for any fixed n, the sequence
{i(n, ... A Combinatorial Proof of the Log-concavity of a
famous sequence counting permutations
Mikl´os B´ona
∗
Submitted: Nov 24, 2004; Accepted: Jan...
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 ... left-hand (resp. right-hand) side of (2).
The aim of this paper is to find a combinatorial proof of (2). In Section 2 we construct
the sets F
bi
n
of...
Báo cáo toán học: "A Combinatorial Proof of a Symmetric q-Pfaff-Saalsch¨ tz Identity u" pps
... generalization of the famous q-Pfa-Saalschăutz identity. An elementary
proofofthisidentityisalsogiven.
1 Introduction
Throughout this paper we regard q as an indeterminate, and we follow the notation ... electronic journal of combinatorics 12 (2005), #N2 4
A Combinatorial Proof of a Symmetric
q-Pfa-Saalschăutz Identity
Victor J. W. Guo
Center for Combinatorics, LPMC
Nankai...
Báo cáo toán học: "A Simple Proof of the Aztec Diamond Theorem" potx
... 1986.
the electronic journal of combinatorics 12 (2005), #R18 8
Theorem 2.3 (Aztec diamond theorem) The number of domino tilings of the Aztec
diamond of order n is 2
n(n+1)/2
.
Remark: The proof of ... between domino tilings of an Aztec diamond and non-
intersecting lattice paths, a simple proof of the Aztec diamond theorem is given by
means of...
Báo cáo toán học: "A short proof of a theorem of Kano and Yu on factors in regular graphs" pot
... and y. Then G is a 4 -regular graph, and G has a 1-factor con-
taining e and a 1-factor avoiding e. According to Theorem 3, G has a k-factor containing
e and a k-factor avoiding e for every k ... containing e and a 1-factor avoiding e, then G has a k-factor containing e and a k-factor
avoiding e for every k ∈ {1, 2, . . . , r − 1}.
Proof. Let F and F
e
be two...
Báo cáo toán học: "A Combinatorial Proof of Andrews’ Smallest Parts Partition Function" ppsx
... of parts of λ is
called the length of λ, denoted by l(λ). The weight of λ is the sum of parts, denoted by
|λ|. We let P(n) denote the set of partitions of n.
Let spt(n) denote the number of smallest ... give a combinatorial proof of Andrews’ smallest parts partition function with
the aid of rooted partitions introduced by Chen and the author.
1 Introductio...
Báo cáo toán học: "A Bijective Proof of a Major Index Theorem of Garsia and Gessel" doc
... (2010), #R64 6
A Bijective Proof of a Major Index Theorem
of Garsia and Gessel
∗
Mordechai Novi ck
Department of Mathematics
Hebrew University, Jerusalem, Israel
mordecha.novick@mail.huji.ac.il
Submitted: ... lemma we prove the theorem by establishing a bijection between shuffles
of ordered sequences and a certain set of partitions. A special case of Ga...
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