Henri Mühle has authored 6 sequences.
A292853
Congruence-uniform lattices whose alternate order is a lattice.
Original entry on oeis.org
1, 1, 0, 1, 1, 2, 3, 8, 16, 41, 107, 304, 891, 2735
Offset: 1
- A. Day, Characterizations of finite lattices that are bounded-homomorphic images or sublattices of free lattices, Canadian Journal of Mathematics, 31 (1979), 617-631.
- H. Mühle, On the lattice property of shard orders, arXiv:1708.02104 [math.CO], 2017.
- N. Reading, Lattice theory of the poset of regions, Birkhäuser, 2016, pages 465-467.
A292790
Congruence-uniform lattices on n unlabeled nodes.
Original entry on oeis.org
1, 1, 1, 2, 4, 9, 22, 60, 174, 534, 1720, 5767, 20013, 71545
Offset: 1
A292852
Spherical congruence-uniform lattices on n unlabeled nodes.
Original entry on oeis.org
1, 1, 0, 1, 1, 2, 3, 8, 17, 45, 123, 367, 1148, 3792
Offset: 1
A280891
Number of certain noncrossing set partitions.
Original entry on oeis.org
1, 4, 12, 37, 118, 387, 1298, 4433, 15366, 53924, 191216, 684114, 2466428, 8951945, 32683230, 119949945, 442281030, 1637618400, 6086481720, 22699003830, 84918443220, 318593346630, 1198421583684, 4518886787802, 17077448924828, 64671604514552, 245380598678208, 932708665735364, 3551238550341944, 13542393822575541
Offset: 1
X_4 has the following 10 elements: 1|2|3|4, 12|3|4, 1|23|4, 1|24|3, 14|2|3, 1|234, 124|3, 14|23, 134|2, 1234. The a(2)=4 elements in which 2 and 3 are in the same block are 1|23|4, 1|234, 14|23, 1234.
- Andrew Howroyd, Table of n, a(n) for n = 1..500
- H. Gao and R. Schiffler, On the Number of τ-Tilting Modules over Nakayama Algebras, SIGMA 16 (2020), 058.
- H. Mühle, Two Posets of Noncrossing Partitions Coming From Undesired Parking Spaces, arXiv:1701.02109 [math.CO], 2017.
- Murray Tannock, Equivalence classes of mesh patterns with a dominating pattern, MSc Thesis, Reykjavik Univ., May 2016.
- Qi Wang, Tau-tilting finite simply connected algebras, arXiv:1910.01937 [math.RT], 2019.
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CoefficientList[Series[(1 + x) (1 - 3 x - (1 - x) Sqrt[1 - 4 x])/(2 x^2), {x, 0, 30}], x] (* Michael De Vlieger, Jan 03 2020 *)
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C(n)=binomial(2*n,n)/(n+1);
vector(66,n,C(n + 1) - C(n - 1)) \\ Joerg Arndt, Apr 19 2017
A274778
Number of proper mergings of an n-antichain and an n-chain.
Original entry on oeis.org
0, 3, 26, 442, 12899, 582381, 37700452, 3315996468, 380835212037, 55380159334315, 9950025870043126, 2165134468142294430, 561245519520167902471, 170913803045738754172185, 60421582956702701927410120, 24543570079301728283314502248, 11353373604627607560431407875081
Offset: 0
For n=1, the three proper mergings of a 1-chain {x} and a 1-antichain {y} are x<y, y<x, and x,y.
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a := n -> add(((n-i+1)^n-(n-i)^n)*(i+1)^n, i=0..n):
seq(a(n), n=0..16); # Peter Luschny, Nov 11 2016
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a[0] = 0; a[n_] := Sum[((n-i+1)^n - (n-i)^n)*(i+1)^n, {i, 0, n}];
Table[a[n], {n, 0, 16}] (* Jean-François Alcover, Jul 14 2018, after Peter Luschny *)
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a(n) = sum(i=1, n+1, ((n+2-i)^n - (n+1-i)^n)*i^n); \\ Michel Marcus, Jul 14 2018
A215582
The number of proper mergings of two n-antichains.
Original entry on oeis.org
1, 3, 35, 1275, 154115, 71994363, 140595475715, 1133624776334235, 36970581556591250435, 4838797912961323412254203, 2535793883977350841761956006915, 5317221866238397002010248863448839835, 44602260230569982664472646479956459441496835, 1496585236610867406252010206465708857876795888774523
Offset: 0
For n=1, the a(1)=3 proper mergings of two 1-antichains ({a},{}) and ({b},{}) are the following three posets: ({a,b},{}), ({a,b},{(a,b)}), ({a,b},{(b,a)}).
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Table[Sum[Sum[Sum[If[i+j+k==n,n!/(i!j!k!)*(-1)^k*(2^i+2^j-1)^n,0],{i,0,n}],{j,0,n}],{k,0,n}],{n,0,20}] (* Vaclav Kotesovec, Aug 23 2012 *)
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