Self-orthogonal diagonal latin squares

Author: kref

August undefined, 2024

WebNumber of self-orthogonal diagonal Latin squares of order n with the first row in ascending order. 6 1, 0, 0, 2, 4, 0, 64, 1152, 224832, 234255360 ( list ; graph ; refs ; listen ; history ; text ; internal format ) WebSep 12, 2011 · A Doubly Self Orthogonal Latin Square (DSOLS) is a Latin square which is orthogonal to its transpose to the diagonal and its transpose to the back diagonal. It is …

On the existence of self-orthogonal diagonal Latin …

WebNov 27, 2024 · A Latin square A is called self-orthogonal if A and A T are orthogonal Latin squares. Use the elements of Z v as the names of the rows and columns of your Latin square. Let A = ( a i j) such that a i j = 2 i − j ∈ Z v. Prove that this forms a self-orthogonal … WebA Latin square is self-orthogonal if it is orthogonal to its transpose. A diagonal Latin squar... A diagonal Latin square is a Latin square whose main diagonal and back diagonal are … bubbles in phlegm meaning

EXTENDING FREITAG’S FIBONACCI–LIKE MAGIC SQUARE TO …

WebDec 27, 2024 · An n × n matrix A consisting of nonnegative integers is a general magic square of order n if the sum of elements in each row, column, and main diagonal is the same. A general magic square A of order n is called a magic square, denoted by MS ( n ), if the entries of A are distinct. WebDepartment of Computer Science, University of Iowa, Iowa City, IA. Department of Computer Science, University of Iowa, Iowa City, IA. View Profile WebShow that the diagonal elements of a self-orthogonal Latin square must be distinct. Expert Answer Proof A Latin square oforder v is a v × v array such that every row and every column is a permutation ofa v-set S, say S = {0; 1,....v,−1}. Two Latin squares of order v are orthogonal if each symbol … View the full answer export import from india

Transversals of Latin Squares - Mathematics Stack Exchange

WebJan 15, 1996 · A general bound A Latin square is self-orthogonal if it is orthogonal to its transpose. A self- orthogonal Latin square (SOLS) of order v will be denoted by SOLS (v). We also denote by (v, n)-ISOLS an incomplete self-orthogonal Latin square: A Latin square is symmetric if it is equal to its transpose. WebApr 23, 2024 · 1 Use the elements of $\;\mathbb {Z}_v$ as the names of the rows and columns of your Latin square. Let $\boldsymbol {A}= (a_ {ij})$ such that $a_ {ij}=2i-j\in \mathbb {Z}_v$. This forms a self-orthogonal Latin square always when the $\gcd (v,6)=1$, so it works for the order $5$ case as well. Share Cite Follow answered Nov 27, 2024 at … export import germanyWebJun 1, 2011 · A diagonal Latin square is a Latin square whose main diagonal and back diagonal are both transversals. A Latin square is self-orthogonal if it is orthogonal to its … export import forms

"WebFeb 10, 2024 · Download LatinSquares for free. Makes small order Latin squares. Makes small order Latin squares, LS, and diagonal Latin squares, DLS, of various types: LS, DLS, axial symmetric, double axial symmetric, center symmetric, orthogonal, self-orthogonal, natural order first row and first column, self-transpose, associative Here LS exclude DLS, … " - Self-orthogonal diagonal latin squares

Self-orthogonal diagonal latin squares

Incomplete self-orthogonal latin squares - Cambridge Core

WebA Doubly Self Orthogonal Latin Square (DSOLS) is a Latin square which is orthogonal to its transpose to the diagonal and its transpose to the back diagonal. It is challenging to find … WebMar 24, 2024 · Specifically, a Latin square consists of sets of the numbers 1 to arranged in such a way that no orthogonal (row or column) contains the same number twice. For example, the two Latin squares of order two are …

Did you know?

WebApr 15, 2016 · A latin square is represented as t i = ( r, c, s) which means that r represents row of the latin square, c represents column of the latin square and s is the number whose location is r o w = r a n d c o l u m n = c. Share Cite Follow answered Apr 15, 2016 at 7:43 sayan 237 1 5 Add a comment You must log in to answer this question. WebThe diagonal sums are the same as those of the rows and columns because latin square A is orthogonal to both B and C, and one diagonal of A has all entries 0 and the other diagonal has all entries a+1. Latin Squares. Latin Squares: An Introduction. Latin Squares (An Interactive Gizmo) Two Simple Problems with Latin Squares; Latin Squares ...

WebDec 4, 2024 · Diagonal Latin squares ( abbr. DLS) are a special case of LS where in addition to the difference in the values of the elements in the rows and columns, an additional … WebA Latin square is self-orthogonal if it is orthogonal to its own transpose. (i) Prove that the elements on the main diagonal of a SOLS (self-orthogonal Latin square) of order n form a …

WebApr 9, 2009 · Incomplete self-orthogonal latin squares - Volume 42 Issue 3. To save this article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account.

http://cut-the-knot.org/arithmetic/latin3.shtml

Web@inproceedings{Wang1978OnSL, title={On self-orthogonal Latin squares and partial transversals of Latin squares /}, author={Shinmin Wang}, year={1978} } Shinmin Wang; Published 1978; Mathematics; No Paper Link Available. Save to Library Save. Create Alert Alert. Cite. Share This Paper. 39 Citations. Highly Influential Citations. 6. export import hazardous waste regulationWebidempotent square. A diagonal Latin square is a transversal Latin square whose back diagonal also forms a transversal. Two Latin squares ofordervare orthogonalifeach symbol in the rst square meets each symbol in the second square exactly once when they are superposed. A Latin square is self-orthogonal ifit is orthogonal to its transpose. export import inbox rules outlookWebApr 1, 2003 · A latin square which is Δr - and Δℓ -complete is called diagonal-complete, abbreviated to Δ -complete. A concept closely related to completeness and Δ -completeness, but without the latin square structure, has been introduced by Knuth [4]. He calls an n × n -matrix ( aij) a balanced neighbourhood square, if for all eight nonzero … bubbles in photographyWebE. I. Vatutin, List of all main classes of doubly self-orthogonal diagonal Latin squares of orders 1-10. E. I. Vatutin, A. D. Belyshev, About the number of self-orthogonal (SODLS) and doubly self-orthogonal diagonal Latin squares (DSODLS) of orders 1-10. High-performance computing systems and technologies. Vol. 4. No. 1. 2024. pp. 58-63. (in ... bubbles in polyurethane when dryingWebIf A, B, Care 3 MOLS such that B = AT and C = CT, then A is a self-orthogonal Latin square (SOLS) with C a symmetric orthogonal mate (SOM). The set of A, B, C is denoted SOLSSOM. If C has constant diagonal, the SOLSSOM is called unipotent. The existence problem for ISOLS(v, n) has been almost completely solved. The export import indonesia 2022WebIt is a standard fact that for non-zero elements α ∈ F, the formula L α ( x, y) = x + α y produces a latin square. Furthermore, L α and L α ′ are MOLS, if α ≠ α ′. The diagonal … export import india bookWebA self-orthogonal diagonal Latin square is a diagonal Latin square orthogonal to its transpose. A333367(n) <= a(n) <= A309598(n) <= A305570(n). - Eduard I. Vatutin, Apr 26 … bubbles in plastic