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Apr 16 at 15:26 comment added JP McCarthy @PeterTaylor this well answers the question I would have asked.
Apr 16 at 13:44 comment added Peter Taylor FWIW, the question of whether an integer sequence or table has been studied before can often be answered with a search on OEIS. Here $m\diamond n$ corresponds to A305720, so other people have thought about it, but there are no references given to published papers.
Apr 12 at 16:07 comment added Gerald Edgar However note: A post which is off topic will not magically become on-topic simply by adding "Has this been done before?" We sometimes also see this ploy in hsm.stackexchange.com
Jan 17 at 9:59 history edited JP McCarthy CC BY-SA 4.0
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Jan 17 at 9:59 comment added JP McCarthy @JohnBentin they have these basic properties "by transport".
Jan 17 at 9:58 comment added JP McCarthy @LSpice thank you: I just made up the notation on the spot, so just went for an "at hand" notation.
Jan 16 at 20:43 comment added LSpice TeX note: it will produce very large spacing, so maybe you are intentionally avoiding it, but TeX forgets that + is a binary operation when it is \boxed, and \mathbin reminds it: $r\boxed+s$ vs. $r\mathbin{\boxed+}s$ $r\boxed+s$ vs. $r\mathbin{\boxed+}s$. But perhaps just $r \boxplus s$ r \boxplus s (although there is only $r \boxtimes s$ r \boxtimes s, not a boxed star, as far as I know) will do?
Jan 16 at 16:11 comment added John Bentin Not your question, I know, but a primary reason to study any proposed new structure is that it is interesting. The richness of much of mathematics arises from the basic operations interacting through simple laws: in particular, the distribution of multiplication over addition and the associative law for both operations. Do your operations conform to such laws?
Jan 15 at 17:36 vote accept JP McCarthy
Jan 12 at 19:23 answer added Neil Strickland timeline score: 33
Jan 12 at 18:45 history became hot meta post
Jan 10 at 20:26 history asked JP McCarthy CC BY-SA 4.0