Hall, M. (1967) Combinatorial Theory. Wiley and Sons, New York and London.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a strategy which minimizes this congestion measure. First we justify why cong( x) is a measure of goodness for a state x: 1. If the current state is x; every packet has duration T units and there is no future arrival, then the minimum time taken to transfer all waiting packets is Tcong( x) [5, 16]. 2. We have shown in section 3 that the optimal policy minimizes a parametrized function J ;OPT ( x) referred to as the discounted loss rate function for each state x and all values of a certain parameter 1: We show here that under heavy trac this function is lower bounded by cong( x) for ....

M. Hall Jr. Combinatorial Theory. John Wiley and Sons, 1998.

....the p s are the positional representation of the code. To show that all minimal length codes are based on difference sets, set c = a b for a and b as defined in Property 5. There is a faster method of searching for minimal length OOC s based on difference sets and the theory of multipliers [4, 5]. Definition 3 Let (t, #) 1 where ( means the greatest common factor and let s be an arbitrary integer. Then an integer t is a multiplier of the (#, K, #) difference set D = p 1 , p 2 , p K if there exists an integer s such that E = tp 1 , tp 2 , tp K and # = p 1 s, p 2 ....

Hall, M., Jr., Combinatorial Theory, Blaisdell, 1967.

....a complete classification of the resolvable 3 (14, 7, 5) designs. Theorem 1 A resolvable t (2k, k, #) design with t even is a resolvable (t 1) 2k, k, # # ) design with # # = #(k t) 2k t) and vice versa. Prior to this classification only one resolvable 2 (14, 7, 12) design was known [3, 5]. Further definitions and background results on resolvable designs are given in Section 2. Of central importance is a correspondence between resolutions of designs and certain error correcting codes due to Semakov and Zinov ev [10] Section 3 outlines the classification algorithm, which is based ....

M. Hall, Jr., Combinatorial Theory, Blaisdell, Waltham, 1967.

....is a maximal 3 set of MOLS of order 8t 1 for every positive integer t 5 such that 6t 1 is a prime power. Proof. Suppose that 6t 1 is a prime power and that t 3; 5. By Theorem 3. 2, there is a V (3; 2t) The existence of a set of 3 MOLS of order 2t is well known for t 3; 5 (see, e.g. [11]) Thus, Lemma 3.1 yields the existence of a 3 set of (8t 1; 2t) MOLS. By Corollary 2.5, this 3 set is maximal. The existence of a maximal 3 set of MOLS of order 9 (the case with t = 1) is known (see [9, p. 387] Theorem 3.4 (Colbourn [6, Theorem 3.1] Let s and r be positive integers with s6r ....

M. Hall Jr., Combinatorial Theory, Blaisdell, Waltham, 1967.

....is smaller. We propose a strategy which minimizes this congestion measure. First we justify why this is a good measure to minimize. If the current state is x; every job has duration T units and there is no future arrival, then the minimum time taken to transfer all waiting jobs is T cong( x)[5, 13]. This indicates that higher the value of cong( x) more congested is the switch in some sense. Next, we present lemma 1 which shows the optimal discounted cost function J ( x) is lower bounded by cong( x) under heavy traffic. Lemma 1 Let the total arrival rate at(intended for) each ....

M. Hall Jr. Combinatorial Theory. John Wiley and Sons, 1998.

....and its existence can always be proved through combinatorial arguments although, for certain memory sizes, explicit constructions can be given. In contrast, all the other graphs employed in the scheme require expansion properties that can be obtained by suitable modifications of the BIBD graph [Hal86] and can always be explicitly constructed. For an n tuple of variables to be read written, the selection of the copies to be accessed and the subsequent execution of the accesses of the selected copies are performed on the D BSP through a protocol similar to the one in [PPS00] which can be ....

M. Hall Jr. Combinatorial Theory. John Wiley & Sons, New York NY, second edition, 1986.

....propose a strategy which minimizes this congestion measure. First we justify why is a measure of goodness for a state #x. 1) If the current state is #x, every packet has duration T units and there is no future arrival, then the minimum time taken to transfer all waiting packets is Tcong(#x) [4], 16] This indicates that higher the value of cong(#x) more congested is the switch in some sense. 2) We show in technical report [13] that the optimal policy minimizes a parametrized function J #,OPT (parameter #) referred to as the discounted loss rate function for each state #x and all ....

M. Hall Jr. Combinatorial Theory. John Wiley and Sons, 1998.

..... Define J v Q[x, t]tobethespan Qf m,d . 12.2. Lemma. Fix d, m 1. Then d (1 If v 1 then Q[x] 12.2.2) where Q[x] denotes the polynomials which are annihilated by # x , that is, the polynomials of degree 1. 12.3. Proof. We use the fact [H86] 1.1 that for any polynomial p, p(k) 0ifdegp n ifp(k) k . 12.3.1) 28 Since C ab = C ba we may express f m,d as: C ab # b (a b)x C ab (a b) b # d # a m b) a b) where b # = b ....

M. Hall, Combinatorial Theory (second edition), John Wiley & Sons, New York (1986).

.... triple systems and has regular features, such that c j = 1 for all j#N a ij = 3 for all i M and = 1 for all j 1 and j 2 (j 1 j 2 ) STS instances can be generated recursively from instances called A 3 and A 15 , where the rule to generate A 3y from an instance A y is found in [14]. A 135 and A 243 were taken from OR Library, and A 405 and A 729 were generated by ourselves from A 135 and A 243 , respectively. The perl script to generate large STS instances from existing STS instances is obtained from our WWW site . Because of its symmetry, all relative costs c j (u ) ....

M. Hall, Jr., Combinatorial Theory, Blaisdell Company, Waltham, MA, 1967.

....has a transitive group of automorphisms of order 360. The research by the first author was supported by NSERC of Canada, Grant No. OGP0008651. 1 Introduction We assume at the outset that the reader is familiar with the basic facts and ideas of design theory as given, for example, in [2] and [9]. A (v; k; graph is a strongly regular (v; k; graph. Thus it is a graph G with v vertices and whose adjacency matrix A satisfies A = k Gamma )I J; where I and J are the identity and all one matrix, respectively. Since A = AA the above equation may be interpreted as saying that A ....

M. Hall, Jr, Combinatorial Theory, Second Edition, John Wiley & Sons, 1986.

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Hall, M. (1967) Combinatorial Theory. Wiley and Sons, New York and London.

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M. Hall Jr. Combinatorial Theory. Blaisdell, Waltham, Massachusetts, 1967.

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Marshall Hall Jr. Combinatorial Theory. Ginn-Blaisdell, Waltham, 1967.

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M. Hall, "Combinatorial Theory," Blaisdell Publishing Company, 1967.

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J. Marshall Hall, Combinatorial Theory. New York: John Wiley & Sons, second ed., 1986.

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M. Hall, Jr., Combinatorial Theory, 2nd ed., John Wiley & Sons, New York, 1986.

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M. Hall. Combinatorial Theory, John Wiley, 1986.

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M. Hall Jr. Combinatorial Theory, Blaisdell, Waltham, Mass., 1967.

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M. Hall. Combinatorial Theory. John Wiley & Sons, 1967.

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M. Hall. Combinatorial Theory. John Wiley & Sons, 1967.

No context found.

M. Hall, Jr., Combinatorial Theory, Waltham, MA, Blaisdell, 1969

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Marshall Hall Jr., Combinatorial Theory, Blaisdell Pub. Co., 1967.

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Hall, M. (1967), Combinatorial Theory, Waltham, MA: Blaisdell Publishing,.

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M. Hall Jr., Combinatorial Theory, Blaisdell, Waltham. Mass., U.S.A., 1967.

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M. Hall, Jr., Combinatorial Theory (2nd ed.), Wiley-Interscience, 1983.

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