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Computing random $r$-orthogonal Latin squares. (English) Zbl 07914101

Wu, Weili (ed.) et al., Combinatorial optimization and applications. 16th international conference, COCOA 2023, Hawaii, HI, USA, December 15–17, 2023. Proceedings. Part II. Cham: Springer. Lect. Notes Comput. Sci. 14462, 165-174 (2024).

MSC: 90C27

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Yadav, Kaushal Kumar; Dash, Sukanta; Mandal, Baidya Nath; Parsad, Rajender

Construction of balanced semi-Latin rectangles in block size four: an algorithmic approach. (English) Zbl 1542.62102

J. Stat. Theory Pract. 18, No. 3, Paper No. 29, 10 p. (2024).

MSC: 62K10 05B15 62K05

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Khattree, Ravindra

Constant and nearly constant block-sum partially balanced incomplete block designs and magic rectangles. (English) Zbl 1517.05031

J. Stat. Theory Pract. 17, No. 1, Paper No. 8, 17 p. (2023).

Reviewer: Paola Bonacini (Catania)

MSC: 05B15 05B05

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Inpoonjai, Phaisatcha; Jiarasuksakun, Thiradet

On the existence of degree-magic labellings of the $n$-fold self-union of complete bipartite graphs. (English) Zbl 1446.05079

Algebra Discrete Math. 28, No. 1, 107-122 (2019).

MSC: 05C78 05B15

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Dobrovol’skii, N. M.; Dobrovol’skii, N. N.; Rebrova, I. Yu.; Balaba, I. N.

Latin rectangles and quadrature formulas. (English) Zbl 1415.05027

Eur. J. Comb. 80, 82-88 (2019).

MSC: 05B15

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Zhou, Chen; Li, Wen; Zhang, Yong; Su, Renwang

Existence of magic 3-dimensional rectangles. (English) Zbl 1401.05053

J. Comb. Des. 26, No. 6, 280-309 (2018).

Reviewer: John Lorch (Muncie)

MSC: 05B15

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Zhou, Chen; Li, Wen; Zhang, Yong; Su, Renwang

Existence of centre-complementary magic rectangles. (English) Zbl 1387.05029

Discrete Math. 341, No. 7, 1952-1958 (2018).

MSC: 05B15

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Díaz, Mateo; Bras, Ronan Le; Gomes, Carla

In search of balance: the challenge of generating balanced Latin rectangles. (English) Zbl 1489.68251

Salvagnin, Domenico (ed.) et al., Integration of AI and OR techniques in constraint programming. 14th international conference, CPAIOR 2017, Padua, Italy, June 5–8, 2017. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 10335, 68-76 (2017).

MSC: 68T20 05B15 90C11 90C27

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Falcón, Raúl M.

Enumeration and classification of self-orthogonal partial Latin rectangles by using the polynomial method. (English) Zbl 1315.05023

Eur. J. Comb. 48, 215-223 (2015).

MSC: 05B15 05A15

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Stones, Douglas S.; Wanless, Ian M.

Divisors of the number of Latin rectangles. (English) Zbl 1230.05065

J. Comb. Theory, Ser. A 117, No. 2, 204-215 (2010).

MSC: 05B15

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de Gennaro, Aurelio

How many Latin rectangles are there? (English) Zbl 1226.05068

Far East J. Math. Sci. (FJMS) 37, No. 2, 105-132 (2010).

MSC: 05B15 05A15

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De Los Reyes, J. P.; Das, Ashish; Midha, Chand K.; Vellaisamy, P.

On a method to construct magic rectangles of even order. (English) Zbl 1197.05017

Util. Math. 80, 277-284 (2009).

MSC: 05B15

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Cao, H.; Dinitz, J.; Kreher, D.; Stinson, D. R.; Wei, R.

On orthogonal generalized equitable rectangles. (English) Zbl 1283.05042

Des. Codes Cryptography 51, No. 3, 225-230 (2009).

MSC: 05B15 94A60

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Häggkvist, Roland; Johansson, Anders

Orthogonal Latin rectangles. (English) Zbl 1152.05019

Comb. Probab. Comput. 17, No. 4, 519-536 (2008).

Reviewer: Peter Horák (Tacoma)

MSC: 05B15

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de los Reyes, J. P.; Das, Ashish; Midha, Chand K.

A matrix approach to construct magic rectangles of even order. (English) Zbl 1170.05019

Australas. J. Comb. 40, 293-300 (2008).

Reviewer: A. Rosa (Hamilton/Ontario)

MSC: 05B15 05B99

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Stinson, D. R.

Generalized mix functions and orthogonal equitable rectangles. (English) Zbl 1179.05022

Des. Codes Cryptography 45, No. 3, 347-357 (2007).

MSC: 05B15 94A60

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Grechannikov, A. V.

New algorithms for calculation of logarithmic estimates for $(0,1)$-matrix permanents and their application to problems of chemical kinetics and combinatorial analysis. (English) Zbl 1092.65039

Russ. J. Numer. Anal. Math. Model. 21, No. 1, 39-52 (2006).

MSC: 65F40 05C50

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Murugesan, R.; Thamarai Selvi, S.; Alphonse Rajendran, P.; Sampath Kumar, V. S.

Identification of a rank minimal optimal sequence for open shop scheduling problems. (English) Zbl 1050.90523

Int. J. Inf. Manage. Sci. 14, No. 1, 37-55 (2003).

MSC: 90B35 90C57

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Timashov, A. N.

On permanents of random doubly stochastic matrices and asymptotic estimates of the numbers of Latin rectangles and Latin squares. (English. Russian original) Zbl 1048.05016

Discrete Math. Appl. 12, No. 5, 431-452 (2002); translation from Diskretn. Mat. 14, No. 4, 65-86 (2002).

MSC: 05B15 05A16 60J10 15B51 15A15

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Sonnino, A.

Some results on generalised affine spaces and their applications. (English) Zbl 1019.51002

Dattoli, Giuseppe (ed.) et al., Advanced special functions and integration methods. Proceedings of the workshop, Melfi, Italy, June 18-23, 2000. Rome: Aracne Editrice. Proc. Melfi Sch. Adv. Top. Math. Phys. 2, 339-350 (2001).

Reviewer: Vito Napolitano (Potenza)

MSC: 51A15

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Bräsel, Heidemarie; Harborth, Martin; Willenius, Per

Isomorphism for digraphs and sequences of shop scheduling problems. (English) Zbl 0983.90018

J. Comb. Math. Comb. Comput. 37, 115-128 (2001).

MSC: 90B35 05C60 05C20 05B15

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Bailey, R. A.; Monod, H.

Efficient semi-Latin rectangles: designs for plant disease experiments. (English) Zbl 0973.62061

Scand. J. Stat. 28, No. 2, 257-270 (2001).

Reviewer: R.E.Maiboroda (Kyïv)

MSC: 62K10 62P10

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Buravlev, S. M.

Matchings up to the permutations which form a Latin rectangle. (English. Russian original) Zbl 0968.60021

Discrete Math. Appl. 10, No. 1, 23-48 (2000); translation from Diskret. Mat. 12, No. 1, 24-46 (2000).

Reviewer: Alexander V.Bulinskij (Moskva)

MSC: 60F05 05B15

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Ali, Asghar

A construction method for balanced $6\times6$ Graeco-Latin designs with a set of 4 treatments superimposed on a $6\times6$ Latin square. (English) Zbl 1128.05301

Pakistan J. Stat. 15, No. 3, 155-166 (1999).

MSC: 05B15 62K10

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Chappell, Glenn G.

A matroid generalization of a result on row-Latin rectangles. (English) Zbl 0933.05034

J. Comb. Theory, Ser. A 88, No. 2, 235-245 (1999).

Reviewer: Yuri Chebrakov (St.Peterburg)

MSC: 05B35

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Wanless, Ian M.

Permanents, matchings and Latin rectangles. (English) Zbl 0920.05010

Bull. Aust. Math. Soc. 59, No. 1, 169-170 (1999).

MSC: 05B15 05C50 05C70 05E35 15A15 15B51

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Skau, Ivar

A note on the asymptotic number of Latin rectangles. (English) Zbl 0905.05003

Eur. J. Comb. 19, No. 5, 617-620 (1998).

Reviewer: L.A.Székely (Columbia/South Carolina)

MSC: 05A16 05B15

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Mckay, B. D.; Wanless, I. M.

Maximising the permanent of $(0,1)$-matrices and the number of extensions of Latin rectangles. (English) Zbl 0887.05011

Electron. J. Comb. 5, Research paper R11, 20 p. (1998); printed version J. Comb. 5, 161-180 (1998).

Reviewer: A.K.Lal (Kanpur)

MSC: 05B15 05C70 15A15 15B36

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Mahmoodian, E. S.; van Rees, G. H. J.

Critical sets in back circulant latin rectangles. (English) Zbl 0881.05030

Australas. J. Comb. 16, 45-50 (1997).

Reviewer: Peter Boyvalenkov (Sofia)

MSC: 05B15

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Donovan, Diane; Hoffman, D. G.

Critical sets in a family of groups. (English) Zbl 0881.05029

Australas. J. Comb. 16, 21-28 (1997).

Reviewer: Peter Boyvalenkov (Sofia)

MSC: 05B15

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Liebler, Robert A.; Magliveras, Spyros S.; Tsaranov, Sergei V.

Block transitive resolutions of $t$-designs and Room rectangles. (English) Zbl 0883.05014

J. Stat. Plann. Inference 58, No. 1, 119-133 (1997).

Reviewer: E.R.Lamken (Pasadena)

MSC: 05B05 05B15 05B07

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Robinson, John P.

Golomb rectangles as folded rulers. (English) Zbl 0869.94029

IEEE Trans. Inf. Theory 43, No. 1, 290-293 (1997).

MSC: 94A99 05B15

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Zeng, Jiang

The generating function for the difference in even and odd three-line Latin rectangles. (English. Extended French summary) Zbl 0863.05019

Ann. Sci. Math. Qué. 20, No. 1, 105-108 (1996).

Reviewer: Ph.Biane (Paris)

MSC: 05B15 05A15

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Evans, Anthony B.

Magic rectangles and modular magic rectangles. (English) Zbl 0851.05031

J. Stat. Plann. Inference 51, No. 2, 171-180 (1996).

Reviewer: G.Bonanno (Davis)

MSC: 05B15 05B99

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Song, Hong-Yeop; Dinitz, Jeffrey H.

Tuscan squares. (English) Zbl 0845.05023

Colbourn, Charles J. (ed.) et al., The CRC handbook of combinatorial designs. Boca Raton, FL: CRC Press. CRC Press Series on Discrete Mathematics and its Applications. 480-484 (1996).

Reviewer: K.Engel (Rostock)

MSC: 05B30 05B15

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Colbourn, Charles J.; Dinitz, Jeffrey H.

Latin squares. (English) Zbl 0870.05008

Colbourn, Charles J. (ed.) et al., The CRC handbook of combinatorial designs. Boca Raton, FL: CRC Press. CRC Press Series on Discrete Mathematics and its Applications. 97-110 (1996).

Reviewer: C.J.Salwach (Easton)

MSC: 05B15

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Cooke, Ch. H.

An extended class of resolvable, incomplete lattice designs. (English) Zbl 0889.05022

Ars Comb. 44, 161-172 (1996).

Reviewer: A.Drápal (Praha)

MSC: 05B15 05B20

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Chow, Timothy Y.

On the Dinitz conjecture and related conjectures. (English) Zbl 0854.05020

Discrete Math. 145, No. 1-3, 73-82 (1995).

Reviewer: J.Bierbrauer (Houghton)

MSC: 05B15 05B20

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McKay, Brendan D.; Rogoyski, Eric

Latin squares of order 10. (English) Zbl 0824.05010

Electron. J. Comb. 2, Note N3, 3 p. (1995); printed version J. Comb. 2, 427-429 (1995).

MSC: 05B15

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Shearer, James B.

Some new optimum Golomb rectangles. (English) Zbl 0821.05006

Electron. J. Comb. 2, Research paper R12, 9 p. (1995); printed version J. Comb. 2, 189-197 (1995).

MSC: 05B15 94A99

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Suchower, Stephan J.

Nonisomorphic complete sets of $F$-rectangles with prime power dimensions. (English) Zbl 0818.05016

Des. Codes Cryptography 5, No. 2, 155-174 (1995).

Reviewer: B.L.Raktoe (Singapur)

MSC: 05B15

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Suchower, Stephan J.

Nonisomorphic complete sets of F-rectangles with varying numbers of symbols. (English) Zbl 0808.05017

Mullen, Gary L. (ed.) et al., Finite fields: theory, applications and algorithms. 2nd international conference, August 17-21, 1993, Las Vegas, NV, USA. Providence, RI: American Mathematical Society. Contemp. Math. 168, 353-362 (1994).

Reviewer: J.Dénes (Budapest)

MSC: 05B15 11T06

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Preece, D. A.

Triple Youden rectangles: A new class of fully balanced combinatorial arrangements. (English) Zbl 0808.05026

Ars Comb. 37, 175-182 (1994).

Reviewer: H.J.Tiersma (Diemen)

MSC: 05B30 05B15 05B05

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Preece, D. A.

Double Youden rectangles – an update with examples of size $5\times 11$. (English) Zbl 0796.05014

Discrete Math. 125, No. 1-3, 309-317 (1994).

MSC: 05B15

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Christofi, C.

Enumerating $4\times 5$ and $5\times 6$ double Youden rectangles. (English) Zbl 0796.05013

Discrete Math. 125, No. 1-3, 129-135 (1994).

MSC: 05B15

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Bräsel, H.; Kluge, D.; Werner, F.

A polynomial algorithm for the $[n/m/0,\;t_{ij}=1,\text{ tree}/C_{\max}]$ open shop problem. (English) Zbl 0798.90081

Eur. J. Oper. Res. 72, No. 1, 125-134 (1994).

MSC: 90B35

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Jacroux, Mike

A note on constructing magic rectangles of even order. (English) Zbl 0793.05026

Ars Comb. 36, 335-340 (1993).

MSC: 05B15

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Janssen, Jeannette C. M.

The Dinitz problem solved for rectangles. (English) Zbl 0792.05053

Bull. Am. Math. Soc., New Ser. 29, No. 2, 243-249 (1993).

MSC: 05C15 05A05 05B15

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Bier, Thomas; Rogers, Douglas G.

Balanced magic rectangles. (English) Zbl 0782.05014

Eur. J. Comb. 14, No. 4, 285-299 (1993).

Reviewer: J.Dénes (Budapest)

MSC: 05B15

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Mullen, Gary L.; Purdy, David

Some data concerning the number of Latin rectangles. (English) Zbl 0782.05016

J. Comb. Math. Comb. Comput. 13, 161-165 (1993).

Reviewer: József Dénes (Budapest)

MSC: 05B15 05A15

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Shevelev, V. S.

Reduced Latin rectangles and square matrices with equal sums in rows and colums. (Russian) Zbl 0768.05017

Diskretn. Mat. 4, No. 1, 91-110 (1992).

Reviewer: K.Burian (Havířov)

MSC: 05B20 05B15

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Mandeli, John P.

Complete sets of mutally orthogonal frequency rectangle designs having twice a prime power number of columns. (English) Zbl 0755.05014

Util. Math. 41, 151-160 (1992).

Reviewer: S.Lajos (Budapest)

MSC: 05B15

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Bräsel, H.; Kleinau, M.

On the number of feasible schedules of the open-shop-problem – an application of special Latin rectangles. (English) Zbl 0817.90034

Optimization 23, No. 3, 251-260 (1992).

MSC: 90B35

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Bräsel, H.; Kleinau, M.

On number problems for the open shop problem. (English) Zbl 0788.90037

Kall, Peter (ed.), System modelling and optimization. Proceedings of the 15th IFIP conference, Zurich, Switzerland, September 2-6, 1991. Berlin: Springer-Verlag. Lect. Notes Control Inf. Sci. 180, 145-154 (1992).

MSC: 90B35