The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.

## Filters

##
###
Page 1317 of Mathematical Reviews Vol. , Issue 96c
[page]

1996
*
Mathematical Reviews
*

Summary: “It is proved in this paper that for any integer n > 53, there exist 3 IMOILS (

*three*incomplete*mutually**orthogonal**idempotent**Latin**squares*) if and only if v > 4n.” 96c:05026 05B15 Roberts, Charles ... E., Jr. (1-INS; Terre Haute, IN) Sets*of**mutually**orthogonal**Latin**squares*with “like subsquares”. ...##
###
Page 7323 of Mathematical Reviews Vol. , Issue 97M
[page]

1997
*
Mathematical Reviews
*

42, 46, 54, 58, 62, 66, 70, 94}.”
97m:05049 05B15
Zhang, Xiafu (PRC-KIT; Kunming);
Zhang, Hangfu (1-SCA; Los Angeles, CA)

*Three**mutually**orthogonal**idempotent**Latin**squares**of**order**18*. ... Summary: “*Three**mutually**orthogonal**idempotent**Latin**squares**of**order**18*are constructed, which can be used to obtain 3 HMOLS*of*type 5'* and type 23'* and to obtain a (90,5, 1)-PMD.” 97m:05050 05B20 94899 ...##
###
Page 2086 of Mathematical Reviews Vol. , Issue 98D
[page]

1998
*
Mathematical Reviews
*

98d:05034
notice that

*idempotent**orthogonal*arrays*of*strength two are*idempotent**mutually**orthogonal*quasigroups. Then, we state some properties*of**idempotent**orthogonal*arrays. ... Mappings*of**Latin**squares*. (English summary) Linear Algebra Appl. 261 (1997), 251-268. Summary: “Let L, denote the set*of*n by n*Latin**squares*. ...##
###
A lower bound on permutation codes of distance n-1
[article]

2019
*
arXiv
*
pre-print

A classical recursive construction for

arXiv:1902.04153v2
fatcat:thut5fnrgrfdfiu6hecw4udvji
*mutually**orthogonal**latin**squares*(MOLS) is shown to hold more generally for a class*of*permutation codes*of*length n and minimum distance n-1. ... When such codes*of*length p+1 are included as ingredients, we obtain a general lower bound M(n,n-1) > n^1.079 for large n, gaining a small improvement on the guarantee given from MOLS. ... Theorem 2. 3 . 3 If there exist r*mutually**orthogonal**idempotent**latin**squares**of**order*n, then there exists an r-IPC(n, n − 1). Proof. ...##
###
Latin Squares with Self-Orthogonal Conjugates

2004
*
Discrete Mathematics
*

In this paper, we investigate the existence

doi:10.1016/j.disc.2003.11.022
fatcat:lxnbrhdsofhl5fgxzjxovalr2y
*of**idempotent**Latin**squares*for which each conjugate is*orthogonal*to precisely its own transpose. ... As an application*of*our results, it is shown that for all integers v ¿ 8, with the possible exception*of*10 and 11, there exists an*idempotent**Latin**square**of**order*v that realizes the one-regular graph ... Acknowledgements The ÿrst author would like to acknowledge the support*of*the Natural Sciences and Engineering Research Council*of*Canada under NSERC Grant OGP0005320 and the second author would like to ...##
###
Difference Covering Arrays and Pseudo-Orthogonal Latin Squares

2015
*
Graphs and Combinatorics
*

We will use this connection to settle the spectrum question for sets

doi:10.1007/s00373-015-1649-8
fatcat:lc4uqq2hvzf5fbcwumafdssg6u
*of*3*mutually*pseudo-*orthogonal**Latin**squares**of*even*order*, for all but the*order*146. ... A special class*of*pseudo-*orthogonal**Latin**squares*are the*mutually*nearly*orthogonal**Latin**squares*(MNOLS) first discussed in 2002, with general constructions given in 2007. ... A set*of*t*Latin**squares*,*of**order*n, are said to be*mutually*pseudo-*orthogonal*if they are pairwise pseudo-*orthogonal*. ...##
###
Incomplete conjugate orthogonal idempotent latin squares

1987
*
Discrete Mathematics
*

Let us denote by COILS(v) a (3, 2, 1)-conjugate

doi:10.1016/0012-365x(87)90207-x
fatcat:5fmdqjyzs5eotpm2lm3ev7z4s4
*orthogonal**idempotent**Latin**square**of**order*v, and by ICOILS(v, n) an incomplete COILS(v) missing a sub-COILS(n). ... The construction*of*an ICOILS(8, 2) has already been instrumental in the construction*of*a COILS(26), the existence*of*Which was unknown for some time. A necessary condition for the existence*of*an. ... Acknowledgment The first author acknowledges the financial support*of*the Natural Sciences and Engineering Research Council*of*Canada under grant A-5320. ...##
###
Further results on incomplete (3,2,1)- conjugate orthogonal idempotent Latin squares

1990
*
Discrete Mathematics
*

Acknowledgements The first author would like to thank the organizing committee

doi:10.1016/0012-365x(90)90267-l
fatcat:ps7mfunm6vavtnyzn4gvxjjhce
*of*the Third Chinese Combinatorial Conference and the Mathematics Department*of*Suzhou University for their kind hospitality ... A portion*of*this work was carried out earlier while the second author was a visiting professor at Mount Saint Vincent University, and he gratefully acknowledges the hospitality accorded him. ...*of*T(k + 1, 1; m) or k -1*mutually**orthogonal**Latin**squares*(MOLS)*of**order*m. ...##
###
Resolvable bibd and sols

1983
*
Discrete Mathematics
*

Resolvable grid systems can be constructed from

doi:10.1016/0012-365x(83)90003-1
fatcat:xr6bapk2gvchzfybhqrhlcji6i
*mutually**orthogonal*self-*orthogonal**latin**squares*(SOLS) with symmetric mate. ... Together these results prove, as a special case, that: if k -1 is an odd prime power and there exist J(k -2)*mutually**orthogonal*SOLS*of**order*n, with symmetric mate, then there exists a resolvable BIBD ... For the remainder*of*Ithis paper 'a set*of*SOLS' will mean a set*of**mutually**orthogonal*self-*orthogonal**latin**squares*, all*idempotent*, and the phrase 'h SOL!? ...##
###
Complementary partial resolution squares for Steiner triple systems

2003
*
Discrete Mathematics
*

array formed by the superposition

doi:10.1016/s0012-365x(02)00471-5
fatcat:3bo5l7zinvbethed6fofw7auba
*of**three**mutually**orthogonal**Latin**squares**of**order*v where v ≡ 1 (mod 6), v ≥ 7, and v / ... Our main result is the existence*of*six complementary partial resolution*squares*for Steiner triple systems*of**order*v which can be superimposed in a v × v array so that the resulting array is also the ... Acknowledgments Research*of*E.R. Lamken was supported by NSF grant DMS9753244. ...##
###
Page 6542 of Mathematical Reviews Vol. , Issue 2003i
[page]

2003
*
Mathematical Reviews
*

A Vi(m,t) leads to m

*idempotent*pairwise*orthogonal**Latin**squares**of**order*(m7 +1)t+1 with one common hole*of**order*t. For m= 3,4,5,6 and 7 the spectrum for V(m,t) has been de- termined. ... The author generalizes the notion*of*a transversal*of*a*Latin**square*by defining a k-plex to be a partial*Latin**square**of**order*n containing kn entries such that each row and column contains exactly k ...##
###
Page 18 of Mathematical Reviews Vol. 55, Issue 1
[page]

1978
*
Mathematical Reviews
*

self

*orthogonal**Latin**squares*(SOLS)*of**order*n having a symmetric and*idempotent*mate. (2) (kn, k, k—1)*of*size k and (n(k—1), k, k/2)*of*size kK—1, when k—1=3 (mod 4) is a prime power and there are ... Self-*orthogonal**Latin**squares*and BIBD’s. ...##
###
Conjugate orthogonal quasigroups

1978
*
Journal of combinatorial theory. Series A
*

INTRODUCTION The construction

doi:10.1016/0097-3165(78)90074-2
fatcat:r2gopbovcjefnoc2j6mzelaajq
*of**orthogonal*quasigroups, or equivalently*orthogonal**latin**squares*, has long been an area*of*intense mathematical research, culminating in the celebrated disproof*of*the ... A quasigroup (S, .)*of**order*n is equivalent to an O&n, 3) with (i, j, k) as a row if and only if i *j = k. There are other characterizations*of*quasigroups,*latin**squares*, and*orthogonal*arrays. ...##
###
The number of the non-full-rank Steiner triple systems
[article]

2018
*
arXiv
*
pre-print

We derive a formula for the number

arXiv:1806.00009v1
fatcat:petcjh7mo5cutcgzu7yq6q5n4e
*of*different Steiner triple systems*of**order*v and given 2-rank r_2<v and the number*of*Steiner triple systems*of**order*v and given 3-rank r_3<v-1. ... The p-rank*of*a Steiner triple system B is the dimension*of*the linear span*of*the set*of*characteristic vectors*of*blocks*of*B, over GF(p). ...*of**idempotent*totally symmetric*latin**squares**of**order*u), Π u is the number*of*symmetric*latin**squares**of**order*u, Λ u is the number*of**latin**squares**of**order*u. ...##
###
Mutually orthogonal latin squares with large holes
[article]

2014
*
arXiv
*
pre-print

More generally, if a set

arXiv:1410.6743v1
fatcat:khupxleg3fbgfaqrifx7yubfgu
*of*t incomplete*mutually**orthogonal**latin**squares**of**order*n have a common hole*of**order*m, then n > (t+1)m. ... Two*latin**squares*are*orthogonal*if, when they are superimposed, every*ordered*pair*of*symbols appears exactly once. ... For prime powers q, there exist q − 2*mutually**orthogonal**idempotent**latin**squares**of**order*q. ...
« Previous

*Showing results 1 — 15 out of 215 results*