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JCT
2008

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There exists no Steiner system S(4, 5, 17)

13 years 11 months ago

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If a Steiner system S(4, 5, 17) exists, it would contain derived S(3, 4, 16) designs. By relying on a recent classification of the S(3, 4, 16), an exhaustive computer search for S...

Patric R. J. Östergård, Olli Pottonen

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Id	Views	Title	Status

1	138	There exists no Steiner system S(4, 5, 17)	claim
2	132	The absolute order on the symmetric group, constructible partially ordered sets and Cohen-Macaulay complexes	claim
3	120	Approximate min-max theorems for Steiner rooted-orientations of graphs and hypergraphs	claim
4	111	Few-cosine spherical codes and Barnes-Wall lattices	claim
5	109	Decomposing Berge graphs and detecting balanced skew partitions	claim
6	109	Spanning 3-colourable subgraphs of small bandwidth in dense graphs	claim
7	103	A bijective proof of Jackson's formula for the number of factorizations of a cycle	claim
8	101	Refined activation strategy for the marking game	claim
9	100	Optimal distortion embeddings of distance regular graphs into Euclidean spaces	claim
10	96	Asymptotic enumeration of dense 0-1 matrices with specified line sums	claim
11	96	Graphs with full rank 3-color matrix and few 3-colorings	claim
12	92	3-Uniform hypergraphs of bounded degree have linear Ramsey numbers	claim
13	91	A chain theorem for matroids	claim
14	87	End spaces of graphs are normal	claim
15	86	On distinguishing trees by their chromatic symmetric functions	claim
16	86	The maximum edit distance from hereditary graph properties	claim
17	85	A bound on the size of separating hash families	claim
18	85	Smith normal form and Laplacians	claim
19	84	Fix-Mahonian Calculus, II: Further statistics	claim
20	84	Minimally non-Pfaffian graphs	claim
21	84	Wild triangles in 3-connected matroids	claim
22	83	Bounds on degrees of p-adic separating polynomials	claim
23	81	Algebraic characterization of uniquely vertex colorable graphs	claim
24	79	Packing d-degenerate graphs	claim
25	78	A partition bijection related to the Rogers-Selberg identities and Gordon's theorem	claim
26	77	Counting descent pairs with prescribed tops and bottoms	claim
27	76	Quadruple systems with independent neighborhoods	claim
28	76	Bisimplicial vertices in even-hole-free graphs	claim
29	74	Claw-free graphs. V. Global structure	claim
30	71	Primitive decompositions of Johnson graphs	claim
31	70	The number of possibilities for random dating	claim
32	70	Connectivity keeping edges in graphs with large minimum degree	claim
33	70	Bruhat order, smooth Schubert varieties, and hyperplane arrangements	claim
34	70	Claw-free graphs. IV. Decomposition theorem	claim
35	68	Matroids with nine elements	claim
36	68	An Ore-type theorem on equitable coloring	claim
37	68	Pseudo 2-factor isomorphic regular bipartite graphs	claim
38	67	On the number of directions determined by a pair of functions over a prime field	claim
39	67	A lower bound for the length of a partial transversal in a Latin square	claim
40	65	Random graphs on surfaces	claim
41	64	Alternating subgroups of Coxeter groups	claim
42	63	On the chromatic number of an oriented matroid	claim
43	62	A Schur function identity related to the (-1)-enumeration of self-complementary plane partitions	claim
44	62	Generalized quasirandom graphs	claim
45	62	Linked graphs with restricted lengths	claim
46	62	Connectivity of addable graph classes	claim
47	61	Enumerating split-pair arrangements	claim
48	59	The Jones polynomial and graphs on surfaces	claim
49	59	Partition identities and the coin exchange problem	claim
50	58	Monochromatic Hamiltonian Berge-cycles in colored complete uniform hypergraphs	claim
51	58	Sharp thresholds for the phase transition between primitive recursive and Ackermannian Ramsey numbers	claim
52	57	On generalized separating hash families	claim
53	57	Partially directed paths in a wedge	claim
54	57	Invariant boundary distributions for finite graphs	claim
55	57	k-Ordered Hamilton cycles in digraphs	claim
56	55	Claw-free graphs. II. Non-orientable prismatic graphs	claim
57	55	Packing of graphs with small product of sizes	claim
58	54	Nowhere-zero 3-flows in triangularly connected graphs	claim
59	53	A major index for matchings and set partitions	claim
60	53	Exact sequences for the homology of the matching complex	claim
61	50	Eigenvalue bounds for independent sets	claim
62	48	On small blocking sets and their linearity	claim
63	46	A new short proof of a theorem of Ahlswede and Khachatrian	claim
64	46	A multi-dimensional approach to the construction and enumeration of Golay complementary sequences	claim
65	46	Simple permutations and algebraic generating functions	claim
66	46	Claw-free graphs. III. Circular interval graphs	claim
67	44	No four subsets forming an N	claim
68	44	Quasi-isometries between graphs and trees	claim
69	43	Prime graphs and exponential composition of species	claim
70	42	On sets of integers whose shifted products are powers	claim
71	39	Sets of elements that pairwise generate a linear group	claim
72	37	Generating weakly 4-connected matroids	claim
73	35	Maximal periods of (Ehrhart) quasi-polynomials	claim
74	31	Semi-regular relative difference sets with large forbidden subgroups	claim

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