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Upper bounds for football pool problems and mixed covering codes

Heikki Hämäläinen, Seppo Rankinen
1991 Journal of combinatorial theory. Series A  
INTRODUCTION In this paper we collect upper bounds for football pool problems and mixed covering codes. We consider the space [F: [Fi, with t, b 3 0, t + b 2 1.  ...  If b = 0, the problem is usually referred to as the football pool problem. We present upper bounds for K(t, b, R) when t + b 6 13 and R 6 3.  ...  covering radius of the (0, 12,80)2 code of Section 3 is indeed 2.  ... 
doi:10.1016/0097-3165(91)90024-b fatcat:343jdtumojcalk3nnkuqxnxhuu

Bounds on packings and coverings by spheres inq-ary and mixed Hamming spaces

G.J.M. van Wee
1991 Journal of combinatorial theory. Series A  
We concentrate on general q-ary codes and on binary/ ternary mixed codes. Special attention is paid to the football pool problem; a few new lower bounds are established.  ...  In a recent paper by the same author general improvements on the sphere covering bound for binary covering codes were obtained.  ...  The covering problem for qi = 3 (for all i) and R = 1 is also well-known as the football pool problem (for n matches).  ... 
doi:10.1016/0097-3165(91)90010-e fatcat:oke22xxlgzcilerdfghnelhtdy

Page 2050 of Mathematical Reviews Vol. , Issue 98C [page]

1998 Mathematical Reviews  
The results include the following upper bound for the football pool problem for 9 matches: K(9,1) < 1356.  ...  A 56 (1991), no. 1, 84— 95; MR 911:94045] presented a table of upper bounds for such binary/ternary mixed covering codes.  ... 

Page 2357 of Mathematical Reviews Vol. , Issue 92d [page]

1992 Mathematical Reviews  
The author concentrates on q-ary codes (with special attention to the football pool problem) and on binary/ternary mixed codes (which are of practical interest for the football pools).  ...  The authors derive lower [resp. upper] bounds for the cardinality of covering [resp. packing] codes, in the case of binary/ternary mixed Hamming spaces.  ... 

Graph domination, tabu search and the football pool problem

Rowan Davies, Gordon F. Royle
1997 Discrete Applied Mathematics  
We demonstrate the effectiveness of this algorithm by considering a previously studied class of graphs, the so-called "football pool" graphs, and improving many of the known upper bounds for this class  ...  We describe the use of a tabu search algorithm for generating near minimum dominating sets in graphs.  ...  often called the football pool problem.  ... 
doi:10.1016/s0166-218x(96)00049-2 fatcat:tzpqbwo7mjfnvpi546i4e2kkca

Page 1460 of Mathematical Reviews Vol. , Issue 99b [page]

1991 Mathematical Reviews  
Football pools occupy a brief chapter, bringing in mixed cover- ings (ternary-binary, to allow for ties and cases where one of the three outcomes can be ruled out).  ...  There is a table of bounds for n < 33 and R < 10. Chapter 7 studies lower bounds on ¢[n, k] and /(m, R) for linear codes.  ... 

Page 5224 of Mathematical Reviews Vol. , Issue 911 [page]

1991 Mathematical Reviews  
This substantially generalizes the results obtained by Delsarte and by Duc for A = 1.” 911:94045 94B75 05A20 Hiamiilainen, Heikki (SF-TURK); Rankinen, Seppo Upper bounds for football pool problems and  ...  mixed covering codes.  ... 

Improving Bounds on the Football Pool Problem by Integer Programming and High-Throughput Computing

Jeff Linderoth, François Margot, Greg Thain
2009 INFORMS journal on computing  
The Football Pool Problem, which gets its name from a lottery-type game where participants predict the outcome of soccer matches, is to determine the smallest covering code of radius one of ternary words  ...  to improve the lower bound on the size of the optimal code from 65 to 71.  ...  Introduction The Football Pool Problem is one of the most famous problems in coding theory (Hämäläinen et al., 1995) and concerns finding small cardinality covering codes.  ... 
doi:10.1287/ijoc.1090.0334 fatcat:45mqzu74ardmrlyew4wcdbbuv4

At the Dawn of the Theory of Codes

Alexander Barg
1993 The Mathematical intelligencer  
We refer to [25] for an overview and comparison of these methods. Perfect Coverings of Hamming Space and a Football-Pool Problem t M = 11F~IJ#{xld(x,A) 0:;: t} = qnJ~C) (ql)i.  ...  The football-pool problem gave birth to a number of articles [30] [31] [32] [33] devoted to the construction of good covering codes.  ... 
doi:10.1007/bf03025254 fatcat:kqoqgrxuxvemdjrbswawuttv4i

Bounds on mixed binary/ternary codes

A.E. Brouwer, H.O. Hamalainen, P.R.J. Ostergard, N.J.A. Sloane
1998 IEEE Transactions on Information Theory  
Upper and lower bounds are presented for the maximal possible size of mixed binary/ternary error-correcting codes. A table up to length 13 is included.  ...  The upper bounds are obtained by applying the linear programming bound to the product of two association schemes. The lower bounds arise from a number of different constructions.  ...  Johnson (see [1] ) and M. Resende (see [13] ) for assistance with clique-finding programs, and M. Szegedy (cf. [39] ) for improving three entries in the tables (see text).  ... 
doi:10.1109/18.651001 fatcat:sar7f7msjjeydc7bsm32w2e6fq

Aggregating Algorithm for prediction of packs

Dmitry Adamskiy, Anthony Bellotti, Raisa Dzhamtyrova, Yuri Kalnishkan
2019 Machine Learning  
We propose a number of merging algorithms for prediction of packs with tight worst case loss upper bounds similar to those for Vovk's Aggregating Algorithm.  ...  Empirical experiments on sports and house price datasets are carried out to study the performance of the new algorithms and compare them against an existing method.  ...  Poor performance of AAP-current on tennis data with small packs and football data calls for an explanation. We attempt to explain this using upper bound (12).  ... 
doi:10.1007/s10994-018-5769-2 fatcat:byeh5tlccrenfciqpbbcz6oybm

Weighted coverings and packings

G. Cohen, I. Honkala, S.N. Litsyn, H.F. Mattson
1995 IEEE Transactions on Information Theory  
Acknowledgements The authors would like to thank Heikki Hamalainen for providing several useful examples presented in this paper and the anonymous referees for helpful suggestions.  ...  For our second application of weighted coverings we consider a generalized football pool problem [28] , [32] .  ...  Weighted coverings can be found in [20) as well, in a construction for mixed perfect codes.  ... 
doi:10.1109/18.476311 fatcat:5mgydqiylfd2dmekdjhwksdvw4

Can immigrants counteract employer discrimination? A factorial field experiment reveals the immutability of ethnic hierarchies

Kåre Vernby, Rafaela Dancygier, Semih Tumen
2019 PLoS ONE  
Going beyond existing work, we test for a large range of applicant characteristics using a factorial design.  ...  How pervasive is labor market discrimination against immigrants and what options do policymakers and migrants have to reduce it?  ...  Acknowledgments We thank Sofia Härd, Erik Antonsson and Martina Zetterqvist for valuable research assistance and participants at seminars at the American Political Science Association, Stanford University  ... 
doi:10.1371/journal.pone.0218044 pmid:31339894 pmcid:PMC6655538 fatcat:mmpcom7m5ffo3nw4kq7omrnt5q

A Column Generation Approach for Graph Coloring

Anuj Mehrotra, Michael A. Trick
1996 INFORMS journal on computing  
We use a column generation method for implicit optimization of the linear program at each node of the branch-and-bound tree.  ...  We present a method for solving the independent set formulation of the graph coloring problem (where there is one variable for each independent set in the graph).  ...  Use a faster code for smaller problems.  ... 
doi:10.1287/ijoc.8.4.344 fatcat:hyfacc7dsffn5pwh5eeyzmxtn4

Not quite fair play, old chap: the complexion of cricket and sport in South Africa

Bill Nasson
2009 Kronos  
On the other hand, however tightly constricted, middleand upper-class females were encouraged to play sport, sometimes on the mixed courts and fairways of middle-class sociability.  ...  Whether in or out of the water, what urban Africans did in their spare time had always been a problem for Native Affairs officials.  ... 
doaj:7bef8ab140c34e99b68415937cb09092 fatcat:6j7s35so4rh23dsgxvoepkwaqy
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