cardinal ordinal and nominal numbers

Ngày tải lên: 25/08/2016, 20:21

Ngày tải lên: 30/08/2016, 10:35

Ngày tải lên: 17/04/2014, 15:05

... calculate dλ and dη by the hook formula, fill λ = λ( ) and η with their respective hook numbers In both, examine the ith row from the bottom - with their respective hook numbers Divide η into B1 and B2 ... sµ (x1 , x2 , · · ·) is the corresponding Schur function, and sµ (1, · · · , 1) is the number µ1 of (semi-standard, i.e rows weakly and column strictly increasing) tableaux of shape µ, filled ... SR(µ), R and µ with their hook numbers For example, when µ = (4, 2, 1) 3 SQ(4, 2, 1) : 4 SR(4, 2, 1) : R(4, 2, 1) : – – 5 4 3 1 the electronic journal of combinatorics no.1 (1997), #R22 and (4,...

Ngày tải lên: 07/08/2014, 06:20

... q-Eulerian numbers For q = they reduce to the Eulerian numbers of type B, and for q = they reduce to the ordinary Eulerian numbers Color-signed permutations From the definition of the q-Eulerian numbers, ... = #{i ∈ [n] : πi < 0} and def P (π) = n − N(π) The well-known Eulerian numbers Ank count permutations in Sn with k descents Similarly, Eulerian numbers of type B are the numbers Bnk of signed ... integer and let σ denote the golden ratio ( − 1)/2 Then ∞ n n−1 (1) m (2m + 1) σ m+2 =σ m=1 −2n bnk σ k , k=1 where the numbers bnk are defined by b1,1 = 1, bnk = for k ≤ and for k > n, and the...

Ngày tải lên: 07/08/2014, 06:20

... contradicting Observation Hence, v6 and v8 have a common neighbor, and so G = F11 Suppose secondly that v5 and v6 , or v7 and v8 , have a common neighbor We may assume that v5 and v6 have a common neighbor; ... Plummer, Factors and Factorization 403–430 Handbook of Graph Theory ed J L Gross and J Yellen CRC Press, 2003, ISBN: 1-58488-092-2 [11] W R Pulleyblank, Matchings and Extension 179–232 Handbook of ... joining {v5 , v6 } and {v7 , v8 } Since each of v5 and v6 is at distance from a degree-4 vertex (namely, v3 and v4 ), d(v5 ) = d(v6 ) = by Observation Further for i ≥ 9, d(v, vi) ≥ 3, and so, by Observation...

Ngày tải lên: 07/08/2014, 13:21

... over the complex number but not the real numbers and over the real numbers but not the rational numbers We use these ideas to construct two matrices, and from these matrices, patterns that have ... if and only if G is a F complete graph, and mr(SG ) = |G| − if and only if G is a path The latter statement is a consequence of Fiedler’s Tridiagonal Matrix Theorem (proved over the real numbers ... linearly dependent, and thus there is a cycle of V containing j and contained in {1, 2, , k, j} Hence, there is a row of CV with a ∗ in column j, and 0s in all positions with > k and = j The result...

Ngày tải lên: 07/08/2014, 15:23

... product of any path and any star, resolving a longˇc standing conjecture by Jendro´ and Sˇerbova in [12] Besides, it has also been helpful l for other works concerning exact crossing numbers (as in ... function of the graphs G1 and G2 at vertices v1 and v2 The zip product of G1 and G2 according to σ is the graph G1 ⊙σ G2 obtained from the disjoint union of G1 − v1 and G2 − v2 after adding edges ... product of graphs Gx and Gy , respectively obtained from t s Gs and Gt by adding a vertex x or y and connecting it to the endvertices of C in Gs or Gt By Menger’s theorem, x and y each has a bundle...

Ngày tải lên: 08/08/2014, 12:22

... λ|θ) (4) As a last generalization of the Stirling and Bell numbers, we would like to mention [34] and the r-Stirling and r-Bell number (see [24] and the references therein) Neither of these two ... −1 D = −X −2 and thus a representation of our variables U, V for s = and h = −1 Considering s = (and h = 1), one has a representation V → X and U → E1 = XD, the Euler operator, and the normal ... Mendez, P Blasiak and K.A Penson, Combinatorial approach to generalized Bell and Stirling numbers and boson normal ordering problem, J Math Phys 46 (2005) Article 083511 [23] M Mendez and A Rodriguez,...

Ngày tải lên: 08/08/2014, 14:23

... E2n (q) (q; q)2n The coefficients T2n+1 (q) and E2n (q) occurring in those expansions are called q-tangent numbers and q-secant numbers, respectively, and known to be PIC polynomials, such that ... q)-analogs of the tangent and secant numbers, respectively They may be regarded as the graded forms of the traditional q-tangent and q-secant numbers T2n+1 (q), En (q) defined in (1.1)q and (1.2)q The ... (resp by T′ ) n D´sir´ Andr´’s main result was to show that tangent and secant numbers were true e e e enumerators for all alternating permutations: #T2n+1 = #T′ 2n+1 = T2n+1 and #T2n = ′ #T2n =...

Ngày tải lên: 08/08/2014, 14:23

... read and write whole numbers to at least 1000 in figures read and write whole numbers to at least 1000 in figures read and write whole numbers to at least 1000 in words read and write whole numbers ... numbers to 1000 order whole numbers to 1000 order whole numbers to 1000 and position them on a number line order whole numbers to 1000 and position them on a number line order whole numbers and ... guard count on and back in ones, tens and hundreds count on and back in twos count on and back in tens count on in fives count on and back in threes count on and back in fours count on and back in...

Ngày tải lên: 31/10/2014, 13:36

Ngày tải lên: 28/08/2016, 17:35

... with a trend and a constant and at the first lag level) 94 x Table 5.3-2 Augmented Dickey Fuller (ADF) tests on individual firms – FHF to SOL (tested with a trend and a constant and at the first ... between stock returns and accounting numbers (Bartholdy et al., 2004’ Easton & Harris, 1991; Penman, 1992;) and (iii) studies devoted to the use of accounting data by investors and to the impact ... However, there are survey and behavioural researches — including Arnold and Moizer (1984), Barker (1999), Govindarajan (1980), Lee and Tweedie (1981), Previts et al (1994) and Yap (1997) — which...

Ngày tải lên: 10/12/2016, 13:47

... least a summand is less than 3; (b) the greatest summand is even; (c) summands and appear times and time, respectively Solution (a) Using Result 3.1 part (a), we have P (8|at least a summand is less ... such that all summands are at least i and at most j Therefore the number of partitions of n, with the even greatest summand is P (n) − n −1 i=1 P (n − 2i|1, 2, , 2i) if n is even and n−1 i=1 P ... that the greatest summand of this partition is m These numbers are P (n − m|1, 2, , m) If we have summand m − 1, the number n − (m − 1) must be partitioned such that any summand is not greater than...

Ngày tải lên: 21/12/2016, 10:54

... TG: Call Vocabulary time and present Months of the year And ask them when is their birthdays Put a sentence on the board: My birthday is on Set a model and ask each student 5) Answer ... Answer the questions below TG: Draw a blank calendar on the board showing the days and weeks of november Explain and count the seven days of the week Vocabulary: time = days of the week Monday;...

Ngày tải lên: 26/08/2016, 15:31

Ngày tải lên: 27/08/2016, 17:53

... digits of the following numbers a) Forty-seven b) Thirteenth c) Ninth d) Eighty e) Seven hundredth Write the following numbers a) 69th ... 120 g) 96 th h) 180 _ 99th 70th 112th Now, listen to five numbers and cross them out (X) Write the missing one on the line a) 23 56 26 12 17 _ th st th ... 69th b) 58th c) 3rd _ d) 29 Listen to one number and cross it out (X) a) 13 23 33 30 nd nd th b) 82 92 28 29th c) 18 80 81 108 d) 60th 50th 30th...

Ngày tải lên: 28/08/2016, 11:04

Ngày tải lên: 17/04/2014, 15:34

Ngày tải lên: 27/08/2016, 06:03

Ngày tải lên: 27/08/2016, 09:33