Báo cáo toán học: "Two-person symmetric whist" pot

Báo cáo toán học: " New proofs of Schur-concavity for a class of symmetric functions" potx

... Provisional PDF corresponds to the article as it appeared upon acceptance. Fully formattedPDF 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 FUNCTIONSHUAN-NAN SHI∗, JIAN ZHANG AND CHUN GUDEPARTMENT OF ELECTRONIC INFORMATION,TEACHER’S ... , n, (4)and established the following results by using Theorem A. NEW PROOFS OF SCHUR-CONCAVITY FOR A CLASS OF SYMMETRIC FUNCTIONS 7[2] Wang, B-Y: Foundations of majorization inequalities,...

Báo cáo toán học: ": ALGEBRAIC MATCHING THEORY" pot

... 1. IntroductionA 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 polynomialà(G, ... of vertices missed by a maximum matching in a graphG is the multiplicity of zero as a root of the matchings polynomial à(G, x)ofG, and hence many results in matching theory can be expressed ... =0thenmult(, G)is the number of vertices in G missed by a maximum matching. Consequently manyclassical results in the theory of matchings provide information related to mult(0,G). Werefer in...

Báo cáo toán học: " Balanced Gray Codes" pot

... [2], we will call a Gray code balanced if for any two bitpositions 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 ... ann-bit binary Gray code can be viewed asa Hamilton path in then-cube and a cyclic binary Gray code as a Hamilton cycle. One suchcyclic Gray code, the Binary Reﬂected Gray Code (BRGC), ... 32 4 8 09 512 56 8 5 410 1024 102 13 8 2Table 1: Values of constants.4-bit Balanced Gray Code 5-bit Balanced Gray Code0000 00000 101111000 10000 101011100 11000 100011101 11100 110011111...

Báo cáo toán học: " Deformation of Chains via a Local Symmetric Group Action" pot

... explicit. Deformation of Chains via a Local Symmetric Group ActionPatricia Hersh∗Department of Mathematics, Room 2-588Massachusetts Institute of Technology77 Massachusetts AvenueCambridge, MA 02139hersh@math.mit.eduSubmitted: ... [El] becausewe it will allow us to explain why orbits of local symmetric group actions onlattices are always products of chains. When a permutation w is written as a product of adjacent transpositionsw ... inSection 2 that the maximal chains in an orbit of a local symmetric group action must be arranged in such a way that they form the skeleton of such a multi-dimensional box. Otherwise, braid relations...

Báo cáo toán học: "The Action of the Symmetric Group on a Generalized Partition Semilattice" potx

... extendsome of the results of Πnby Hanlon and Stanley to Πn,k.Just as there is an action of the symmetric group Sn on Πn, there is also an action on Πn,kwhich permutes the coordinates of each ... [3]). A version of it states that if the homology of a poset Q isconcentrated in a single dimension r, then the character of the action of a group G on the homology of Q is (1)rtimes the Măobius ... this. The action of Sn on P induces a canonical action on both the homology and the Whitney homology of P . For a Cohen-Macaulay poset Q,letβQ: Sn→ End(H(Q)) be the representation with Snaction...

Báo cáo toán học: "New symmetric designs from regular Hadamard matrices" pdf

... regular Hadamard matrix of order 4 and H is a regular Hadamard matrix of order 9 · 4d+1. Therefore, one can obtain a family of regular Hadamard matrices of order 9 · 4d, starting with a regular ... Yamada, Hadamard matrices, sequences, and block designs, in ContemporaryDesign Theory, eds. J.H. Dinitz and D.R. Stinson, John Wiley & Sons, 1992, 431–560. New symmetric designs from regular Hadamard ... CRCPress, 1996.[4] J. D. Fanning, A family of symmetric designs, Discrete Mathematics 146 (1995), pp. 307–312.[5] Y.J. Ionin, Symmetric subdesigns of symmetric designs, Journal of Combinatorial Mathematicsand...

Báo cáo toán học: "Holes in graphs" potx

... number of times ofobtaining pairs satisfying condition 2 in Claim 2.3, and s2is the number of times obtainingpairs satisfying condition 3 in Claim 2.3. Then we obtain a subgraph G(s1,s2)of ... Assuming that H contains no pair satisfying condition 1, we are going to provethat H contains a pair satisfying condition 2. For simplicity, we assume that 1/ is aninteger.Since, in particular, ... 2/12)d(H).Assuming that H contains no pair satisfying conditions 1 or 2, and using the sametechnique as in the proof of Claim 2.1, we can prove that H must contain a pair satisfyingcondition 3.Applying...

Báo cáo toán học: "Monochrome symmetric subsets in 2-colorings of groups" potx

... into two subsets not containing in nite subsets of the form g + Uwhere U = −U. Such subsets were called symmetric and groups that can be partitionedinto 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 symmetric subset of cardinality ... subgroup of arbitrarily large cardinality < |G|.Proposition. In any 2-coloring, every uncountable group G of regular cardinalitycontains either a monochrome symmetric subset of cardinality...

Báo cáo toán học: "Two-person symmetric whist" pot

... idea works well.1.1 The symmetric caseThroughout the paper, we assume that in each suit the players have the same number ofcards. 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 isdetermined in advance, and does not depend on how the cards are played. The advantageof studying symmetric ... m/2+1/4.Now consider the case that every suit in E has a value which is half an integer. Thenfor the hypothesis to hold, the value of E must be at least m/2+1/2. It therefore suﬃcesto show that West...

Báo cáo toán học: "Domino Fibonacci Tableaux" potx

... 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 dominoinsertion 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 Fibonacci ... bijection between standard domino Fibonacci tableaux and domino Fibonacci pathtableaux. Here we describe the inverse of the evacuation map.To begin, think of a Fibonacci domino tableau as a sequence...

Báo cáo toán học: "Factorial Grothendieck Polynomials" potx

... entirely of partitions.For the case à = , where we are expanding a skew Grothendieck polynomial in thebasis of ordinary Grothendieck polynomials, Theorem 3.11 is easily seen to be consistentwith ... remainderof our energies to exhibiting a relationship between the factorial Grothendieck polynomialsstudied here, and the double Grothendieck polynomials, as studied elsewhere. For themost part of ... important theoremabout ordinary Grothendieck polynomials, as it is proven in greater generality in Theorems4.3 and 4.9 of the following section.Theorem 3.4. The ordinary Grothendieck polynomial Gθ(x)...

Báo cáo toán học: "Random Threshold Graphs" potx

... probability that a random threshold graph is Hamiltonian. There isa nice connection between Hamiltonicity and a threshold graph’s creation sequence. For morebackground on Hamiltonian threshold graphs, ... natural, equivalent models for random threshold graphs and usethese models to deduce a variety of properties of random threshold graphs. Specifically, arandom threshold graph G is generated by choosing ... ways to define threshold graphs; we choose this one asparticularly convenient for our purposes.Definition 2.1 (Threshold graph, representation). Let G be a graph. We say that G is a threshold graph...

Báo cáo toán học: "Some symmetric identities involving a sequence of polynomials" potx

... Jan 14, 2010Mathematics Subject Classiﬁcations: 0 5A1 9, 11B68AbstractIn this paper we establish some symmetric identities on a sequence of polynomialsin an elementary way, and some known identities ... electronic journal of combinatorics 17 (2010), #N7 2 Some symmetric identities involving a sequence of polynomials∗Yuan HeDepartment of Mathematics,Northwest University, Xi’an, Shanxi 710069, ... results of Momiyama and Gessel. After that, Sun [11] re-searched a sequence of complex numbers and further extended the results in [1 2]. Mean-while, he also deduced that for m, n ∈ N and x +...

Báo cáo toán học: "Discrete bidding games" potx

... G(a∗, b) for the bidding game in which Alice starts with a bidding chips andthe 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 proportionof the bidding resources is less than R(G). If her proportion of the bidding resources ... both discrete andreal-valued bidding. Contents1 Introduction 21.1 A game of bidding Tic-Tac-Toe . . . . . . . . . . . . . . . . . . . . . . . . 41.2 A game of bidding chess. . . . . . . ....

Báo cáo toán học: "Aperiodic Subtraction Games" potx

... 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 andpartizan, have been proved to be periodic. Our main purpose here is to exhibitconstructively a class of subtraction games which is ... there exists a moveinto B.the electronic journal of combinatorics 18(2) (2011), #P19 8 Aperiodic Subtraction GamesAviezri S. Fraenkel∗Department of Computer Science and Applied MathematicsWe...

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