... Provisional PDF corresponds to the article as it appeared upon acceptance. Fully formatted
PDF and full text (HTML) versions will be made available soon.
New proofs of Schur-concavity for a class of symmetric ... 0,
and then h
(t) ≤ 0, so f (t) is concave on (0, 1).
NEW PROOFS OF SCHUR-CONCAVITY FOR A CLASS OF
SYMMETRIC FUNCTIONS
HUAN-NAN SHI
∗
, JIAN Z...
... 1. Introduction
A k -matching in a graph G is a matching with exactly k edges and the number of k-
matchings in G is denoted by by p(G, k). If n = |V (G)| we dene the matchings polynomial
à(G, ... of vertices missed by a maximum matching in a graph
G is the multiplicity of zero as a root of the matchings polynomial à(G, x)of
G, and hence many results in matching theory can be expressed...
... [2], we will call a Gray code balanced if for any two bit
positions i and j, |TC(i) − TC(j)|≤2. Thus, the BRCG is totally balanced for n =1, 2,
balanced for n =1, 2, 3, but unbalanced for n ≥ 4.
It ... an
n
-bit binary Gray code can be viewed as
a Hamilton path in the
n
-cube and a cyclic binary Gray code as a Hamilton cycle. One such
cyclic Gray code, the Binary Reflected Gray...
... explicit.
Deformation of Chains via a Local Symmetric
Group Action
Patricia Hersh
∗
Department of Mathematics, Room 2-588
Massachusetts Institute of Technology
77 Massachusetts Avenue
Cambridge, MA 02139
hersh@math.mit.edu
Submitted: ... [El] because
we it will allow us to explain why orbits of local symmetric group actions on
lattices are always products of ch...
... extend
some of the results of Π
n
by Hanlon and Stanley to Π
n,k
.
Just as there is an action of the symmetric group S
n
on Π
n
, there is also an
action on Π
n,k
which permutes the coordinates of each ... [3]). A version of it states that if the homology of a poset Q is
concentrated in a single dimension r, then the character of the action of...
... regular Hadamard matrix of order 4 and H is a regular
Hadamard matrix of order 9 · 4
d+1
. Therefore, one can obtain a family of regular
Hadamard matrices of order 9 · 4
d
, starting with a regular ... Yamada, Hadamard matrices, sequences, and block designs, in Contemporary
Design Theory, eds. J.H. Dinitz and D.R. Stinson, John Wiley & Sons, 1992, 431–560.
New symmetric...
... number of times of
obtaining pairs satisfying condition 2 in Claim 2.3, and s
2
is the number of times obtaining
pairs satisfying condition 3 in Claim 2.3. Then we obtain a subgraph G
(s
1
,s
2
)
of ... Assuming that H contains no pair satisfying condition 1, we are going to prove
that H contains a pair satisfying condition 2. For simplicity, we assume that 1/ is an
integer.
Since, in...
... into two subsets not containing in nite subsets of the form g + U
where U = −U. Such subsets were called symmetric and groups that can be partitioned
into two subsets not containing in nite symmetric ... proof of
Theorem 1 is complete.
In [12] it was proved that in any 3-coloring, every uncountable Abelian group G of
regular cardinality contains either a monochrome sy...
... idea works well.
1.1 The symmetric case
Throughout the paper, we assume that in each suit the players have the same number of
cards. Such a card distribution is called symmetric. If this condition ... broken. In a symmetric deal, the number of tricks where the lead is in a given suit is
determined in advance, and does not depend on how the cards are played. The advantage
of studying sym...
... standard domino Fibonacci
tableaux and Fibonacci path tableaux.
Proof. The evacuation algorithm is, by definition, an injection from standard domino
Fibonacci tableaux to domino Fibonacci path ... domino Fibonacci shape. In the domino
insertion algorithm, the P tableau that is created will be a standard domino Fibonacci
tableau and the Q tableau that is created will be a domino Fi...
... entirely of partitions.
For the case à = , where we are expanding a skew Grothendieck polynomial in the
basis of ordinary Grothendieck polynomials, Theorem 3.11 is easily seen to be consistent
with ... remainder
of our energies to exhibiting a relationship between the factorial Grothendieck polynomials
studied here, and the double Grothendieck polynomials, as studied elsewhere. For th...
... probability that a random threshold graph is Hamiltonian. There is
a nice connection between Hamiltonicity and a threshold graph’s creation sequence. For more
background on Hamiltonian threshold graphs, ... natural, equivalent models for random threshold graphs and use
these models to deduce a variety of properties of random threshold graphs. Specifically, a
random threshold graph...
... Jan 14, 2010
Mathematics Subject Classifications: 0 5A1 9, 11B68
Abstract
In this paper we establish some symmetric identities on a sequence of polynomials
in an elementary way, and some known identities ... electronic journal of combinatorics 17 (2010), #N7 2
Some symmetric identities involving
a sequence of polynomials
∗
Yuan He
Department of Mathematics,
Northwe...
... G(a
∗
, b) for the bidding game in which Alice starts with a bidding chips and
the tie-breaking advantage, and Bob starts with b bidding chips. Similarly, G(a, b
∗
) is the
bidding game in which ... of the total bidding
resources is greater than R(G), and she does not have a winning strategy if her proportion
of the bidding resources is less than R(G). If her proportion of the bi...
... Similarly, subtraction games have been proved to b e periodic, both impartial
[2] and partizan subtraction games [5].
The main purpose of this paper is to produce a class of aperiodic subtraction ... many games. In particular, subtraction games, impartial and
partizan, have been proved to be periodic. Our main purpose here is to exhibit
constructively a class of subtraction games wh...