cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A076016 Number of systems with n elements having one binary operation satisfying the equation B(AB)=A (semisymmetric quasigroups).

Original entry on oeis.org

1, 2, 3, 18, 120, 2880, 140256, 20782080, 9569532672, 14175610675200, 74559788174868480
Offset: 1

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Author

Richard C. Schroeppel, Oct 29 2002

Keywords

Comments

Or, Latin squares for which the set of (row,column,symbol) triples is invariant under cyclic permutation of the elements within each triple.

Crossrefs

Extensions

a(10)-a(11) from Ian Wanless, Dec 08 2021

A362382 Number of nonisomorphic right involutory magmas with n elements.

Original entry on oeis.org

1, 1, 3, 16, 475, 100666, 267954164, 7178089200724, 2878905036230723360, 16030557330452794172050567, 1643024454743084814743097053747492, 3003719433250221394022136941323628209106412, 119909786948816191249293422143299520925389900896422044
Offset: 0

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Author

Andrew Howroyd, Apr 17 2023

Keywords

Comments

A magma with element set X is right involutory if (xy)y = x for x,y in X.

Crossrefs

Cf. A001329 (magmas), A076017, A076019, A361720, A362383 (labeled).

Programs

  • PARI
    B(c,k)=sum(j=0, c\2, if(k%2, 1, 2^(c-2*j))*k^j*binomial(c, 2*j)*(2*j)!/(2^j*j!))
    K(v)=my(S=Set(v)); prod(i=1, #S, my(k=S[i], c=#select(t->t==k, v)); B(c,k))
    R(v,m)=concat(vector(#v,i,my(t=v[i], g=gcd(t,m)); vector(g, i, t/g)))
    a(n)={my(s=0); forpart(p=n, my(v=Vec(p), S=Set(v)); s+=prod(i=1, #S, my(m=S[i], c=#select(t->t==m, v)); (K(R(v,m))/m)^c/c!)); s}

A350019 Number of isotopism classes containing semisymmetric Latin squares of order n.

Original entry on oeis.org

1, 1, 1, 2, 2, 7, 33, 557, 26511, 3908091, 1867909542
Offset: 1

Views

Author

Ian Wanless, Dec 08 2021

Keywords

Crossrefs

A350020 Number of species containing semisymmetric Latin squares of order n.

Original entry on oeis.org

1, 1, 1, 2, 2, 7, 28, 366, 13899, 1968997, 934327507
Offset: 1

Views

Author

Ian Wanless, Dec 08 2021

Keywords

Comments

Species (also called "main classes") are the largest natural equivalence classes of Latin squares.

Crossrefs

Showing 1-4 of 4 results.