ogerard
Reputation
1,197
Top tag
Next privilege 2,000 Rep.
 Oct 29 comment Trouble understanding Latin squares and group theory One can also define infinite, uncountable, even continuous quasigroups and varieties of quasigroups and loops that are not defined by a latin square but (for instance) by generators, relations and identities. For an introduction to that see for example works by J. D. H. Smith Postmodern Algebra, works by Mal'cev, Sabinin, etc. Lookup also Moufang relations, Bol Loops. Oct 29 comment Relations between the Latin squares of order n and the groups of order n. You don't take into account that you can permute the rows or the symbols independently of the columns (or vice-versa) and still have a latin square (or rectangle) for that matter. There are evident normalizations, symmetries and overlaps so latin squares/rectangles arising from group Cayley tables will exhibit a lot less variety upon these transformations than latin squares coming from very nonassociative quasigroups and loops. Jun 20 comment Is there an example of nonassociative arithmetic addition? @JoshuaHonig What Martigan and mixedmath say is true but there are two other aspects : 1) in rings, fields and their generalizations (i.e. modules, near-ring, near-fields, k-, there are at least two binary operations, and by analogy with the classical situation, one operation is called addition and the other multiplication. 2) addition is typically associated with the idea of the magnitude of the result being close to the magnitude of the larger of the elements being combined and multiplication with expansion of magnitude (analogy to the area, the volume, a list of possibilities etc.) May 5 comment Finding an equation of circle which passes through three points Are you sure that your solution covers all degenerate cases ? Feb 10 comment Expressing a sequence with two sigma notation $\NN$ does have zero. You don't need to add it. Feb 10 comment Circular permutations - $n$ sitting at a round table without repeating neighbors @0ana : 13524 and 14253 are not related by a rotation but by a reversal. Feb 5 comment The discriminant of an integral binary quadratic form and the discriminant of a quadratic number field Is this something you came up by yourself ? If not, please give the source by respect of the authors. Dec 12 comment zeros of Incomplet Gamma function @TylerHG : these are not zeroes but misinterpretations of underflows. Oct 28 comment What does a non-mathematician need to google to learn more about latin squares in which each number in each row always has a different successor? @hcc23 : I am also interested by your opinion on my sequential solution to your experimental problem. Oct 28 comment What does a non-mathematician need to google to learn more about latin squares in which each number in each row always has a different successor? No you don't miss anything. You spotted a mistake in my terminology. I should have said cyclic (I will edit it), because in the Williams construction described on the H. Bruin page, this is the same array of differences from one column to the next. In fact, this property might be considered a disadvantage if there is an interaction between the properties of your operations and this sequence of difference, making this series of experimental tests not "mixed" or "unbiased" enough. Oct 27 comment What does a non-mathematician need to google to learn more about latin squares in which each number in each row always has a different successor? Dear @hcc23, you just require that the pairs do not repeat horizontally, am I right ? You also don't need to exclude circular pairs (seeing the latin square as a cylinder or a torus) ? Jan 30 comment Proof concerning Latin squares You are welcome. Consider reading a book about problem solving. The one which was fashionable in my time was Polya's, but there a lot of resources available on the web and in libraries. Apr 14 comment Orthogonal Latin Square 6*6 See my answer for a link on the original paper. A physical copy of the journal of the French "Association for l'Avancement des Sciences" is not so easy to find outside France (where most University libraries have it). May 25 comment Non-associative, non-commutative binary operation with a identity what's the point of adding y if it is zero! Are you sure this was what you meant? May 25 comment When $G'$/$G''$ and $G''$ both are cyclic groups @Basil R: you should edit your title and question. May 24 comment A question about integral quadratic forms The left part of your equation is what mathematicians call a (integral) quadratic form. There is a lot of results about the integers n they can represent or not. May 24 comment Prove that if $(ab)^i = a^ib^i \forall a,b\in G$ for three consecutive integers $i$ then G is abelian thanks a lot for these references. We speak of Exponent semigroup, Levi semigroup, etc. What is the operation on these sets? May 23 comment How to split an integral exactly in two parts @Byron: thanks for this careful explanation with references. May 20 comment Probability of a point taken from a certain normal distribution will be greater than a point taken from another? Just to be sure: do you consider the two draws to be strictly independent, i.e. the mechanism simulated by the second draw is not modified or influenced by the value of the first? If this is the case, the problem can be rephrased very simply, while perhaps not realistic. Also note that there is Cross-Validated, the SE site for statistical Q&A. May 20 comment Logic Puzzle of the age of three sons @Amy : see my answer to R. Israel. No this is not a standard, just a possible thought process of the problem's author. As these problems are supposed to make youngsters manipulate properties of integers, this made-up rule is a way to introduce the composite/prime distinction in the problem.