Báo cáo toán học: "On Stanley’s Partition Function" doc
Báo cáo toán học: "On Stanley’s Partition Function" doc
... u(n).
Theorem 3.2 The partition function t(n) is equal to the number of partitions of n with
an even number of even hooks, and the partition function u(n) is equal to the number of
partitions of n ... for
all partitions of n + 1. Let λ be a partition of n + 1 a nd v = (i, j) be any inner corner of
the Young diagram of λ, that is, the removal of the square v gives a Young diagram of a
p...
Báo cáo toán học: "On a Multiplicative Partition Function" pps
... interpreted as a set -partition function. Indeed, by identifying
factors of m = p
1
p
n
with subsets of {1, 2, ,n},weseethatf(n) is equal to the excess
of the number of ways to partition a set S ... 205-
211.
[7] M. V. Subbarao and A. Verma, Some remarks on a product expansion: an unex-
plored partition function, preprint.
[8] H. S. Wilf, Generatingfunctionology, Second Edition, Academi...
Báo cáo toán học: "On Zeilberger’s Constant Term for Andrews’ TSSCPP Theorem" ppsx
... Plane Partitions V: the TSSCPP conjecture, J. Combin. Theory Ser. A 66
(1994), 28–39.
[2] W. Doran, A connection between alternating sign matrices and totally symmetric self-
complementary plane partitions, ... 988–
1007.
[6] W.H. Mills, D.P. Robbins, and H. Rumsey, Self-complementary, totally symmetric plane
partitions, J. Combin. Theory Ser. A 42 (1986), 277–292.
[7] W. G. Morris, Constant...
Báo cáo toán học: "On Certain Eigenspaces of Cographs" docx
... in the theory of star partitions the eigenvalues 0 and −1 are special
cases (cf. [4], chapter 7). Another interesting result is that singular line graphs of trees
can be partitioned into two classes,
Báo cáo toán học: " On a Partition Function of Richard Stanley" pptx
... of partitions of n [1, p. 1], and
∞
n=0
f(n)q
n
=
i1
(1 + q
2i−1
)
(1 − q
4i
)(1 + q
4i−2
)
2
. (2)
Note that t(n) is Stanley’s partition function referred to in the title of this paper.
Stanley’s ... z,y
−1
). (15)
Proof. We shall in the following be dealing with partitions whose parts are all some
given N.Welet¯π be that partition made up of the parts of π that are <N. In...