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Apr
18
awarded  Enlightened
Apr
18
awarded  Nice Answer
Mar
16
comment Constants in a signature
There's a nice exposition of the Oates-Powell Theorem in Hanna Neumann's book "Varieties of Groups." Here is a link to the Bryant paper.
Mar
16
comment Constants in a signature
@KyleGannon thanks, you too. I just learned about thunks recently, and they're useful in functional languages like Scala. You can delay evaluation of an input to a function by making the argument type, say, () => Int instead of just Int. In other words, you pass in a nullary function instead of an Int. Pretty cool, I think.
Mar
16
answered Constants in a signature
Feb
12
revised An intuition connected with Heyting implication
added 8 characters in body
Feb
11
answered An intuition connected with Heyting implication
Jan
17
reviewed Approve The Galois Field for the polynomial $x^3 - 2$.
Jan
17
reviewed Looks OK Prove using epsilon notation that $\lim_{n\to\infty} n\sin\frac {1}{n}=1$
Jan
17
awarded  Custodian
Jan
17
reviewed Looks OK Dihedral Group and Symmetric Group
Jan
17
reviewed Reject Does this series converge?
Dec
29
comment Is there a systematic way of “discovering” an algebra from observations of its universe?
You could say your graph represents a relational structure (rather than an algebraic structure), but the relations depicted are simply congruence classes of modulo arithmetic. All numbers exhibit such relationships. What makes the numbers appearing in your graph special? Are you observing the evolution of a physical system? You mentioned FSM, but are the nodes in your diagram really the only states, or does the system continue to evolve according to the pattern you described? (If it evolves, then you won't have a finite number of states, but that's not necessarily a problem.)
Dec
29
comment Is there a systematic way of “discovering” an algebra from observations of its universe?
Nice picture. Unfortunately, it doesn't describe an algebra. The problem is your "operators" are not operators since they're not defined on the whole universe. For example, if $f(x) = x+6$ (black edges) is an operation, there should be black edges coming out of every node, which is probably not what you want? Maybe $f$ is a partial operation? Then this could be modeled as a partial algebra. Still, what exactly is the universe? ..all numbers showing up in your diagram, and only those numbers? ..or does the system evolve further?
Dec
28
comment Is there a systematic way of “discovering” an algebra from observations of its universe?
Can you please give an example of one of your sets of integers and a "black box?" If you have a set (or "universe") $X$ along with a set $F$ of operations defined on $X$, then you have a universal algebra, $\langle X, F \rangle$. Note: an operation on $X$ is a function $f: X^n \to X$. It's unclear whether your black boxes are operations because you write $b_n: \mathbb{N} \to \mathbb {N}$, so perhaps these functions map outside your original universe "$Q^m$?" (by the way, instead of $Q^m$, you might consider using $X$, or simply $\{0,1,\dots, m-1\}$, which some people denote by $[m]$).
Nov
24
comment name or characterization for the “partition” lattice of integer partitions of some n? (Young lattice row partial order)
Minor point: you probably don't want to call these Hasse diagrams "partition lattices" since they're not lattices. For example, in the poset of partitions of 5, what is the least upper bound of {311, 221}? Perhaps you could call them "partition poset diagrams?" (not to mention, the name "partition lattices" is already taken)
Nov
9
comment Type theory from ground up, first book recomendation
One option for "gaining access" to the HoTT book is to watch Bob Harper's lectures. In fall 2014 he gave a graduate seminar in HoTT at CMU. In Summer 2015, he gave a condensed version at OPLSS. Links to the videos are in the TypeFunc list that I mentioned in my answer below.
Nov
9
revised Type theory from ground up, first book recomendation
deleted 87 characters in body
Oct
9
reviewed Approve What's the probability of choosing a sequence of $4$ numbers, in a particular order?
Oct
9
revised Type theory from ground up, first book recomendation
deleted 21 characters in body