Báo cáo toán học: "Escher''''''''s Combinatorial Patterns" pot
Báo cáo toán học: "On S-decomposable operators " docx
... class="bi x0 y0 w1 h 1" alt =""
Báo cáo toán học: " A Purely Combinatorial Proof of the Hadwiger Debrunner (p, q) Conjectur" docx
... ,q
|Q|
}.
4.Ateverystageofthisconstructionthenumberofpolytopesgrowsbythenumberof
clonings;ifatthatstageonehadRpolytopesthepointchosenwillbeinatleasthR
ofthemandtherewillbeatmost(1−h)Rclonings.Thenumberofpolytopesinthat
stagewillgrowtoatmost(2−h)R.
5.ThusthefinalnumberofpolytopeswillbeatmostN(2−h)
|Q|
.
6.Wewillusethefactthatthenumberofclonedescendantsofanyoneofouroriginal
polytopescannotexceed...
Báo cáo toán học: "RAMANUJAN’S METHOD IN q-SERIES CONGRUENCES" potx
... idea. In all these theorems, the underlying generating functions were either
modular forms or simple linear combinations thereof.
The point of this paper is to show that Ramanujan’s original method ... to an in nite number of congruence theorems including many non-modular
functions defined by q-series.
Our main result is:
Theorem 1. Suppose p is a prime > 3,and0<a<pand b are in...
Báo cáo toán học: "Escher''''s Combinatorial Patterns" pot
... played the game with his father.) Two pieces of
cut potato can serve as the medium on which to carve the motif and its reflected image, and then
these potato stamps are inked and used to produce a ... translations of the
translation block. These symmetries add a geometric layer of complexity to the combinatorial
scheme.
Escher's Case (1)
We first consider Escher's case (1), in whi...
Báo cáo toán học: "Franklin’s argument proves an identity of Zagier" pdf
... which,
miraculously, Franklin’s argument proves at once.
The author wishes to thank George Andrews and Don Zagier for supplying him with
copies of [3] and [8], and also an anonymous referee for ... [1] and
presented in more detail in [8]. Zagier [8] deduces (2) from (8), essentially by carefully
differentiating with respect to x and setting x =1.
Franklin’s argument proves an i...
Báo cáo toán học: "Dumont’s statistic on words" pptx
... similarly.
Question 6.4. For what conditions on a poset P are the statistics des and dmc equidis-
tributed on the set of linear extensions of P?
One might apply another variation of the method ... following
equidistribution result involving the statistics inv (inversions) and maj (major index).
These two statistics belong to the class of Mahonian statistics. (See [8] for further infor-
ma...
Báo cáo toán học: "Toida’s Conjecture is True" doc
... =1,then(S)
1
⊆
∗
n
. Hence this special case of Zibin’s Conjecture is
Toida’s Conjecture, so that Zibin’s Conjecture implies Toida’s Conjecture.
Corollary 2.9 Toida’s Conjecture implies Zibin’s Conjecture.
Proof. ... δ(B)=B, δ is also an isomorphism of
X(
n
,S−∪{(S)
r
: r is a multiple of m})and
X
(
n
,T−∪{(T )
r
: r is a multiple of m}),
the d-th layer of
X(
n
,S −...
Báo cáo toán học: "Words restricted by patterns with at most 2 distinct letters" pptx
... 33111 322 24 → 331 322 2411 → 331 324 221 1
→ 3431 322 211 → 3431 322 211 ∈ [4]
10
(1 12) .
(7)
the electronic journal of combinatorics 9 (2) (20 02) , #R3 15
Corollary 16 For any p ≥ 0
F
v
p,0
(x; 2) = e
x
p
j=0
x
j
j!
.
Proof. ... 121 }, {1 12, 121 }, {1 12, 122 }, {1 12, 21 1}, {1 12, 21 2}, {1 12, 22 1}, { 121 , 21 2}.
Theorem 5 The pairs {111, 1 12} and {111, 121 } are Wilf e...
Báo cáo toán học: "Permutations avoiding two patterns of length three" ppt
... work
of Mansour [14], who computed generating functions for the number of n-permutations
that avoid two distinct patterns of length three and contain exactly one copy of another
pattern of any length.
It ... avoid two distinct patterns of length three and any
additional set of patterns. We begin by showing how to enumerate these permuta-
tions using generating tre...
Báo cáo toán học: "On a combinatorial problem of Asmus Schmidt" pps
... Orthogonal Polynomials and Applications (VII SPOA) (Granada, 1991), J. Comput.
Appl. Math. 49:1–3 (1993), 243–249.
[6] A. L. Schmidt, “Legendre transforms and Ap´ery’s sequences”, J. Austral. Math. ... On a combinatorial problem of Asmus Schmidt
W. Zudilin
∗
Department of Mechanics and Mathematics
Moscow Lomonosov State University
Vorobiovy Gory, GSP-2, Moscow 119992 RUSSIA
URL:...
Báo cáo toán học: "On the combinatorial structure of arrangements of oriented pseudocircles" ppsx
... vertex.
2. The initial vertex of the next edge is v(j, ∓k).
3. Determine the direction of the next edge by the sign of the entry ∓k in list j and
the direction of the preceding edge according to the ... combining the information about the direction of the first edge with the
corresponding crossing yields a rule for the direction of the second edge. If...
Báo cáo toán học: "Packing densities of patterns" ppsx
... symbol of σ.Sincen +1>m, we can select a random subsequence
of σ of length m by first throwing out one of the n + 1 symbols of σ at random and
then randomly selecting a subsequence of length ... the following theorem of
Stromquist. We give a proof which is somewhat shorter than the proof in [1], both
for its own interest and because we will reuse the method of proof when stu...
Báo cáo toán học: "Erd˝s-Ko-Rado theorems for uniform set-partition o systems" pdf
... system.
Generalizations of Theorems 1 and 2 are stated next without proof. The proofs for
these are very similar to the ones used for the original theorems. Indeed, the only change
to the original proofs is ... higher order, intersecting set partitions.
1 Introduction
In this paper, we prove two Erd˝os-Ko-Rado type theorems for systems of uniform set
partitions. They are stated a...
Báo cáo toán học: "Kocay’s lemma, Whitney’s theorem, and some polynomial invariant reconstruction problems" docx
... #R63 29
Kocay’s lemma, Whitney’s theorem, and some
polynomial invariant reconstruction problems
Bhalchandra D. Thatte
Allan Wilson Centre for Molecular Ecology and Evolution,
and Institute of ... (2),
G
F
and
G − u
F
may be replaced by
G
F
and
G − u
F
, respectively.
Tutte [14], [15] proved the reconstructibility of the characteristic polynomial and...
Từ khóa: