Báo cáo toán học: "Bijective proofs for Schur function identities which imply Dodgson’s condensation formula and Pl¨cker u relations" pps
Báo cáo toán học: "Bijective proofs for Schur function identities which imply Dodgson’s condensation formula and Pl¨cker u relations" pps
... #R16
5
Bijective proofs for Schur function identities which
imply Dodgson’s condensation formula and Pl¨ucker
relations
Markus Fulmek
Institut f¨ur Mathematik der Universit¨at Wien
Strudlhofgasse ... obtain
bijective proofs for Dodgson’s condensation formula, Pl¨ucker relations and a recent
identity of the second author.
1 Introduction
Usually, bijective proo...
Báo cáo toán học: " New proofs of Schur-concavity for a class of symmetric functions" potx
... SHIHUANNAN@YAHOO.COM.CN; SFTHUANNAN@BUU.EDU.CN EMAIL ADDRESSES: JZ: SFTZHANGJIAN@BUU.EDU.CN CG: SFTGUCHUN@BUU.EDU.CN
Theorem D. For k = 1, . . . , n, F
n
(x, k) is an Schur- concave function on R
n
+
.
In ... convex function on Ω.
Recall that the following so-called Schur s condition is very useful for determining
whether or not a given function is Schur- convex or Schur- concav...
Báo cáo toán học: " Bijective proofs of the hook formulas for the number of standard Young tableaux, ordinary and shifted" pptx
... short for ‘standard Young
tableau’.)
Proof. Since the formula and all other things that are needed are stated uniformly
for the ordinary and shifted case, also the proof can be formulated uniformly, ... Wien,
Strudlhofgasse 4, A-1090 Wien, Austria.
Submitted: February 20, 1995; Accepted: July 9, 1995
Bijective proofs of the hook formulas for the number of ordinary standard
Young...
Báo cáo toán học: "Bijective Proofs of Identities from Colored Binary Trees" doc
... =
m
5n+m
5n+m
n
recently proposed by Sun.
1 Introduction
Recently, by using generating functions and Lagrange inversion formula, Sun [2] deduced
the following identity involving generalized Catalan number C
m,5
(n) ... even number, it is clear that CB
n
⊆ ECB
n
. Hence, we have
|ECB
n
| − |OCB
n
| = CB
n
.
From Theorem 2.1 and Formula 2.1, we see that the right side summand of...
Báo cáo toán học: "Automated Proofs for Some Stirling Number Identities" pptx
... g(m, n, k) allows us to verify the recurrence for F (m, n) independently.
Indeed, using the triangular recurrence (1) for S
1
and the obvious relations for factorials,
harmonic numbers, etc. it ... =
(−1)
n−k
q
−k−2m+1
(q
k
−q
m
)
[
k
m
]
q
((k−1)(q
k+1
−1)S
1
(n,k−1)q
m
+k(q
k
−q
m+1
)S
1
(n,k−2))
−q
m+1
−q
m+2
+q
2m+3
+1
.
References
[1] L. Carlitz. q-Bernoulli and Eulerian number...
Báo cáo toán học: "Elementary Proofs for Convolution Identities of Abel and Hagen–Rothe" pps
... exercises.
References
[1] W. Chu, Invers i on Tec hniques and Combinatorial Identities: A quick introduction to
hypergeome tric ev aluations, Math. Appl. 283 (1994), 31 –57.
[2] W. Chu, Generating functions and combinatorial ... for a historical note. The existing proofs for the identities of Abel
and Hagen–Rothe can be summarized as follows:
• The classical Lagrange expansion...
Báo cáo toán học: "Comultiplication rules for the double Schur functions and Cauchy identities" docx
... corresponding symmetric functions of
[21]; cf. formula (3.7) in that paper. Moreover, under the specialization a
i
= −i + 1 for
all i ∈ Z the double Schur functions become the shifted Schur functions of ... using Corollary 3.13. Then multiply the
Schur functions using the classical Littlewood–Richardson rule. Finally, use Theorem 3.20
to represent each Schur function as a series...
Báo cáo toán học: " Spectrum sensing for cognitive radio exploiting spectrum discontinuities detection" potx
... published immediately upon acceptance. It can be downloaded,
printed and distributed freely for any purposes (see copyright notice below).
For information about publishing your research in EURASIP ... to
http://jwcn.eurasipjournals.com/authors/instructions/
For information about other SpringerOpen publications go to
http://www.springeropen.com
EURASIP Journal on Wireless
Communication...
Báo cáo toán học: " Resource reservation for mobile hotspots in vehicular environments with cellular/WLAN interworking" ppt
... to
http://jwcn.eurasipjournals.com/authors/instructions/
For information about other SpringerOpen publications go to
http://www.springeropen.com
EURASIP Journal on Wireless
Communications and
Networking
© ... F
k
(0) = 0 for R
k
> C
L
.
The cumulative distribution function (CDF) of the queue length is then
F (x) =
K
k=1
F
k
(x). (13)
Given certain delay constraint, the queue occu...
Báo cáo toán học: " Resource Allocation for Asymmetric Multi-Way Relay Communication over Orthogonal Channels" potx
... downloaded,
printed and distributed freely for any purposes (see copyright notice below).
For information about publishing your research in EURASIP WCN go to
http://jwcn.eurasipjournals.com/authors/instructions/
For ... Hausl
∗ 1
, Onurcan
˙
I¸scan
1
and Francesco Rossetto
2
1
Institute for Communications Engineering, Technische Universit¨at M¨unchen, 80290 Munich, Germany
2
DLR,...
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