19 problems

Kearnes' isotopy conjecture for F-quasigroups
arXiv@arxiv
Kearnes' conjecture. Every F-quasigroup is isotopic to a Moufang loop.
Conjectureopenisotopy loop-theory quasigroups
0
The covering-number characterization of S-GQPQs
arXiv@arxiv
The covering-number converse conjecture. If
Conjectureopenhypergraph-theory latin-squares quasigroups
1
Couselo-González-Markov-Nechaev conjecture on recursive MDS codes
arXiv@arxiv
A complete $2$ -recursive code of length $n$ is specified by a function $f$ through the recurrence … for $l>2$ , and it is an MDS code when its associated groupoid is a recursively d…
Conjectureopenmds-codes quasigroups recursive-codes
1
Reducibility conjecture for prime-order latin hypercubes with maximal cuboctahedra
arXiv@arxiv
Reducibility conjecture. Every $d$ -dimensional latin hypercube of order $n$ with the maximum number of cuboctahedra is reducible.
Conjectureopencombinatorics latin-hypercubes quasigroups
0
The variety-invariance conjecture for Bol–Moufang homology
arXiv@arxiv
Let $Vij$ and $Wk\ell$ be identities defining the same variety of quasigroups, let $X$ be any quasigroup in that variety, and let $(t,s)$ be a substitution. Write $H_2(X;Vij,t,s)$ …
Conjectureopenbol-moufang-type homology quasigroups
2
Random Steiner quasigroup row-cycle and subsystem conjecture
arXiv@arxiv
Let $S$ be a Steiner quasigroup of order $n$ selected uniformly at random. Let $\ell(S)$ be the length of its longest row cycle, and let $m(S)$ be the size of its largest proper St…
Conjecturesolvedquasigroups random-structures steiner-triple-systems
0
Papadimitriou–Yannakakis' completeness conjecture for minimum generating sets of quasigroups
arXiv@arxiv
Papadimitriou–Yannakakis' conjecture. The minimum generating set problem for quasigroups is $\exists^{\log^2 n}\mathsf{P}$ -complete.
Conjectureopencomputational-complexity limited-nondeterminism quasigroups
0
The logarithmic loss conjecture for non-isomorphic quadratic quasigroups
arXiv@arxiv
Let $\mathbb F$ be the finite field used to define the quadratic quasigroups $Q_{a,b}$ , and consider the demonstrated collection of examples having maximal non-associativity. Logar…
Conjectureopenfinite-fields isomorphism quasigroups
0
Splitting conjecture for set-theoretic Yang–Baxter homology of Rump right quasigroups
arXiv@arxiv
A Rump right quasigroup is a set equipped with the right-quasigroup structure arising in Rump's framework for set-theoretic solutions of the Yang–Baxter equation. Its set-theoretic…
Conjectureopenhomology quasigroups yang-baxter-equation
0
Grošek–Horák conjecture on maximally nonassociative quasigroups
arXiv@arxiv
Let $Q(*)$ be a quasigroup, meaning that for all $a,b\in Q$ there exist unique $x,y\in Q$ such that $a*x=b$ and $y*a=b$ . A triple $(x,y,z)\in Q^3$ is associative if…
Conjecturerefutedfinite-fields nonassociative-algebra quasigroups
1
The fitted asymptotic formula conjecture for peri-Catalan numbers
arXiv@arxiv
Fitted asymptotic formula conjecture. For all generator counts $s$ , the limit exists and approximately satisfies
Conjectureopenasymptotic-combinatorics enumeration quasigroups
0
The monotonicity conjecture for generator-dependent asymptotic limits
arXiv@arxiv
Generator-limit monotonicity conjecture. The sequence $(L_s)$ increases with $s$ .
Conjectureopenasymptotic-combinatorics enumeration quasigroups
0
The monotonicity conjecture for normalized peri-Catalan growth
arXiv@arxiv
Normalized growth monotonicity conjecture. For each fixed $s$ , the sequence $(a^s_n)_{n\geq 1}$ increases monotonically with $n$ .
Conjectureopenasymptotic-combinatorics enumeration quasigroups
0
The asymptotic growth limit conjecture for peri-Catalan numbers
arXiv@arxiv
Asymptotic growth limit conjecture. The indicated limits exist and satisfy
Conjectureopenasymptotic-combinatorics enumeration quasigroups
1
The asymptotic irrelevance conjecture for quasigroup identities
arXiv@arxiv
Asymptotic irrelevance conjecture. In the large, cancellation resulting from the quasigroup identities has a negligible effect on the asymptotic behavior of the peri-Catalan number…
Conjectureopenasymptotic-combinatorics enumeration quasigroups
0
Two-generator conjecture for quadratical quasigroups of form Qn
arXiv@arxiv
Let $Q$ be a quadratical quasigroup of form $Qn$ , for some positive integer $n$ . Two distinct elements of $Q$ generate $Q$ . Two-generator conjecture. If $x,y\in Q$ are distinct, th…
Conjectureopenquasigroups universal-algebra
1
Polynomiality conjecture for medial quasigroups of prime-power order
arXiv@arxiv
Let $k$ be any natural number, let $p$ be a prime, and write $mq(\mathbb Z_p^k)$ for the number of medial quasigroup structures on the elementary abelian group $\mathbb Z_p^k$ , whi…
Conjectureopenenumerative-combinatorics finite-groups quasigroups
1
Vanishing probability of a Latin-square autotopism component
arXiv@arxiv
For $n>0$ , let $S_n$ be the symmetric group on $n$ symbols, let $\mathrm{Atp}(n)$ denote the autotopism group of Latin squares of order $n$ , and let $\mathbb{P}(n)$ be the probabil…
Conjectureopenlatin-squares permutation-groups quasigroups
1
Quasigroup formulation of the Brown–Erdős–Sós conjecture
arXiv@arxiv
Quasigroup formulation of the Brown–Erdős–Sós conjecture. For every $c>0$ , there is a threshold $n_0$ such that if $Q$ has order $n\geq n_0$ , then for every such subset $S$ , whenev…
Conjectureopenextremal-combinatorics quasigroups triple-systems
1