L.M.P.A
Laboratoire de Mathématiques Pures et Appliquées
Joseph Liouville

## Shalom Eliahou

• Equipe : Algèbre
LMPA
Centre Universitaire de la Mi-Voix
50 rue F. Buisson
CS80699
62228 Calais
• Bureau : B115
• Email : Shalom.Eliahou@lmpa.univ-littoral.fr
• Téléphone : 03.21.46.36.57

## Publications

### Articles de revues

1. Wilf's conjecture and Macaulay's theorem (), In J. Eur. Math. Soc., to appear.
2. On the degree of regularity of a certain quadratic Diophantine equation (, , , and ), In Eur. J. Comb., to appear.
3. Near-misses in Wilf's conjecture ( and ), In Semigroup forum, .
4. Equation-regular sets and the Fox-Kleitman conjecture (, , , and ), In Discrete Mathematics, volume 341, 287-298, .
5. A remarkable $20$-crossing tangle ( and ), In Journal of Knot Theory and its Ramifications, volume 26, .
6. Are Monochromatic Pythagorean Triples Unavoidable under Morphic Colorings? (, , and ), In Experimental Mathematics, Taylor & Francis, volume 0, 1-7, . [pdf]
7. On the finiteness of some $n$-color Rado numbers (, , , , and ), In Discrete Math., volume 340, 39-45, . [pdf]
8. Poonen's conjecture and Ramsey numbers ( and ), In Discrete Appl. Math., volume 209, 102-106, . [pdf]
9. On sortable intervals of monomials ( and ), In Analele Univ. Ovidius Constanta Ser. Mat., volume 24, 87-104, .
10. On the $n$-color Rado number for the equation $x_1+x_2+\dots+x_k+c=x_{k+1}$ (, , , , and ), In Math. Comp., volume 85, 2047-2064, . [pdf]
11. On the number of numerical semigroups $\langle a,b\rangle$ of prime power genus ( and ), In Semigroup Forum, volume 87, 171-186, . [pdf]
12. On the mantissa distribution of powers of natural and prime numbers (, and ), In Acta Math. Hungar., volume 139, 49-63, .
13. Mutually describing multisets and integer partitions ( and ), In Discrete Math., volume 313, 422-433, . [pdf]
14. On the problem of Molluzzo for the modulus 4 ( and ), In Integers, volume 12, 723-739, . [pdf]
15. Weak Schur numbers and the search for G. W. Walker's lost partitions (, , and ), In Comput. Math. Appl., volume 63, 175-182, . [pdf]
16. Two-generator numerical semigroups and Fermat and Mersenne numbers ( and ), In SIAM J. Discrete Math., volume 25, 622-630, . [pdf]
17. Matching subspaces in a field extension ( and ), In J. Algebra, volume 324, 3420-3430, . [pdf]
18. Extremal binary matrices without constant 2-squares ( and ), In J. Comb., volume 1, 77-100, .
19. Minimal sumsets in finite solvable groups ( and ), In Discrete Math., volume 310, 471-479, . [pdf]
20. On linear versions of some addition theorems ( and ), In Linear Multilinear Algebra, volume 57, 759-775, . [pdf]
21. Signed permutations and the four color theorem ( and ), In Expo. Math., volume 27, 313-340, . [pdf]
22. On the product of vector spaces in a commutative field extension (, and ), In J. Number Theory, volume 129, 339-348, . [pdf]
23. Michel Kervaire 1927–2007 (, , and ), In Notices Amer. Math. Soc., volume 55, 960-961, .
24. Michel Kervaire (26 avril 1927–19 novembre 2007) (, , and ), In Gaz. Math., 77-82, .
25. Parity-regular Steinhaus graphs ( and ), In Math. Comp., volume 77, 1831-1839, . [pdf]
26. Lune-free knot graphs (, and ), In J. Knot Theory Ramifications, volume 17, 55-74, . [pdf]
27. Matchings in arbitrary groups ( and ), In Adv. in Appl. Math., volume 40, 219-224, . [pdf]
28. Bounds on the minimal sumset size function in groups ( and ), In Int. J. Number Theory, volume 3, 503-511, . [pdf]
29. Some results on minimal sumset sizes in finite non-abelian groups ( and ), In J. Number Theory, volume 124, 234-247, . [pdf]
30. The small sumsets property for solvable finite groups ( and ), In European J. Combin., volume 27, 1102-1110, . [pdf]
31. Sumsets in dihedral groups ( and ), In European J. Combin., volume 27, 617-628, . [pdf]
32. A survey on modular Hadamard matrices ( and ), In Discrete Math., volume 302, 85-106, . [pdf]
33. Old and new formulas for the Hopf-Stiefel and related functions ( and ), In Expo. Math., volume 23, 127-145, . [pdf]
34. On symmetric and antisymmetric balanced binary sequences ( and ), In Integers, volume 5, 6-18, .
35. Minimal sumsets in infinite abelian groups ( and ), In J. Algebra, volume 287, 449-457, . [pdf]
36. On a problem of Steinhaus concerning binary sequences ( and ), In Experiment. Math., volume 13, 215-229, . [pdf]
37. A note on the Hopf-Stiefel function ( and ), In Enseign. Math. (2), volume 49, 117-122, .
38. Optimally small sumsets in finite abelian groups (, and ), In J. Number Theory, volume 101, 338-348, . [pdf]
39. Infinite families of links with trivial Jones polynomial (, and ), In Topology, volume 42, 155-169, . [pdf]
40. Circulant 16-modular Hadamard matrices and Jacobi sums ( and ), In J. Combin. Theory Ser. A, volume 100, 116-135, . [pdf]
41. Three moves on signed surface triangulations (, and ), In J. Combin. Theory Ser. B, volume 84, 118-125, . [pdf]
42. On systems of binomials in the ideal of a toric variety ( and ), In Proc. Amer. Math. Soc., volume 130, 345-351, . [pdf]
43. Circulant modular Hadamard matrices ( and ), In Enseign. Math. (2), volume 47, 103-114, .
44. Restricted sums of sets of cardinality $1+p$ in a vector space over $\mathbf{F}_p$ ( and ), In Discrete Math., volume 235, 199-213, . [pdf]
45. Restricted sumsets in finite vector spaces: the case $p=3$ ( and ), In Integers, volume 1, 2-19, .
46. Modular sequences and modular Hadamard matrices ( and ), In J. Combin. Des., volume 9, 187-214, . [pdf]
47. Signed diagonal flips and the four color theorem (), In European J. Combin., volume 20, 641-646, . [pdf]
48. Sumsets in vector spaces over finite fields ( and ), In J. Number Theory, volume 71, 12-39, . [pdf]
49. Compressible difference lists. An appendix to: "A note on the equation $\theta \overline{ \theta}=n+\lambda\Sigma$" [J.\ Statist.\ Plann.\ Inference \bf 62 (1997), no.\ 1, 21–34] by Eliahou and Kervaire (, and ), In J. Statist. Plann. Inference, volume 62, 35-38, . [pdf]
50. A note on the equation $\theta \overline{ \theta}=n+\lambda\Sigma$ ( and ), In J. Statist. Plann. Inference, volume 62, 21-34, . [pdf]
51. Enumerative combinatorics and coding theory (), In Enseign. Math. (2), volume 40, 171-185, .
52. Corrigendum to: "Barker sequences and difference sets" [Enseign.\ Math. (2) \bf 38 (1992), no.\ 3-4, 345–382; MR1189012 (93i:11018)] ( and ), In Enseign. Math. (2), volume 40, 109-111, .
53. The $3x+1$ problem: new lower bounds on nontrivial cycle lengths (), In Discrete Math., volume 118, 45-56, . [pdf]
54. Barker sequences and difference sets ( and ), In Enseign. Math. (2), volume 38, 345-382, .
55. On Golay polynomial pairs (, and ), In Adv. in Appl. Math., volume 12, 235-292, . [pdf]
56. A new restriction on the lengths of Golay complementary sequences (, and ), In J. Combin. Theory Ser. A, volume 55, 49-59, . [pdf]
57. Minimal resolutions of some monomial ideals ( and ), In J. Algebra, volume 129, 1-25, . [pdf]
58. Symbolic powers of monomial curves (), In J. Algebra, volume 117, 437-456, . [pdf]

### Chapitres de livres

1. On a conjecture of Fox and Kleitman on the degree of regularity of a certain linear equation ( and ), Chapter in Combinatorial and Additive Number Theory II: CANT, New York, NY, USA, 2015 and 2016 (Melvyn Nathanson, ed.), Springer New York, volume 220, .
2. Investigating Monte-Carlo Methods on the Weak Schur Problem (, , , , and ), Chapter in Evolutionary Computation in Combinatorial Optimization (Middendorf, Martin, Blum, Christian, eds.), Springer Berlin Heidelberg, volume 7832, 191-201, . [pdf]
3. Small sumsets in free products of $\Bbb Z/2\Bbb Z$ ( and ), Chapter in Additive number theory, Springer, 105-113, .
4. Matchings in arbitrary groups ( and ), Chapter in Advances in discrete mathematics in Andalusia (Spanish), Serv. Publ. Univ. Cádiz, Cádiz, 91-96, .
5. Zero-sum balanced binary sequences (, and ), Chapter in Combinatorial number theory, de Gruyter, 165-178, .
6. Some extensions of the Cauchy-Davenport theorem ( and ), Chapter in 6th Czech-Slovak International Symposium on Combinatorics, Graph Theory, Algorithms and Applications, Elsevier, volume 28, 557-564, .
7. The second Betti number of an edge ideal ( and ), Chapter in XXXI National Congress of the Mexican Mathematical Society (Spanish) (Hermosillo, 1998), Soc. Mat. Mexicana, volume 25, 115-119, .
8. An algebraic criterion for a graph to be four-colourable (), Chapter in International Seminar on Algebra and its Applications (Spanish) (México City, 1991), Soc. Mat. Mexicana, volume 6, 3-27, .
9. How many equations are needed to define an algebraic curve? (), Chapter in Research program of the XVIIIth national congress of the Mexican Mathematical Society (Spanish) (Mérida, 1984), Soc. Mat. Mexicana, volume 1, 211-219, .
10. A problem about polynomial ideals (), Chapter in The Lefschetz centennial conference, Part I (Mexico City, 1984), Amer. Math. Soc., volume 58, 107-120, .
11. Idéaux de définition des courbes monomiales (), Chapter in Complete intersections (Acireale, 1983), Springer, volume 1092, 229-240, . [pdf]

### Rapports

1. Numerical semigroups of Szemerédi type (, , , and ), Technical report 531, LMPA, .
2. Monomial ideals with tiny squares (, and ), Technical report 530, LMPA, .
3. On the degree of regularity of a certain quadratic Diophantine equation (, , , and ), Technical report 529, LMPA, .
4. Wilf's conjecture and Macaulay's theorem (), Technical report 521, LMPA, .
5. On the problem of Molluzzo for the modulus 4 ( and ), Technical report 448, LMPA, .
6. On the mantissa distribution of powers of natural and prime number (, and ), Technical report 447, LMPA, . [pdf]
7. Weak Schur numbers and the search for G. W. Walker's lost partitions (, , and ), Technical report 443, LMPA, .
8. Two-generator numerical semigroups and Fermat and Mersenne numbers ( and ), Technical report 416, LMPA, .
9. Matching subspaces in a field extension ( and ), Technical report, LMPA, .
10. Extremal binary matrices without constant 2-squares ( and ), Technical report 404, LMPA, . [pdf]
11. Small sumsets in free products of Z 2 Z ( and ), Technical report, LMPA, .
12. On the product of vector spaces in a commutative field extension (, and ), Technical report, LMPA, .
13. Matchings in arbitrary groups ( and ), Technical report, LMPA, .
14. Minimal Sumsets in Finite Solvable Groups ( and ), Technical report, LMPA, .
15. Signed permutations and the four color theorem ( and ), Technical report, LMPA, .
16. Bounds on the minimal sumset size function in groups ( and ), Technical report, LMPA, .
17. Parity-regular Steinhaus graphs ( and ), Technical report, LMPA, .
18. Zerosum balanced binary sequences (, and ), Technical report, LMPA, .
19. Lune-Free Knot Graphs (, and ), Technical report, LMPA, .
20. On symmetric and antisymmetric balanced binary sequences ( and ), Technical report, LMPA, .
21. Old and New Formulas for the Hopf-Stiefel and related Functions ( and ), Technical report, LMPA, .
22. The small sumsets property ( and ), Technical report, LMPA, .
23. Finite Sumsets in Infinite Abelian Groups ( and ), Technical report, LMPA, .
24. Some Results on Minimal Sumset Sizes in Finite Non-Abelian Groups ( and ), Technical report, LMPA, .
25. Sumsets in Dihedral Groups ( and ), Technical report, LMPA, .
26. A note on the Hopf-Stiefel function ( and ), Technical report, LMPA, .
27. On a problem of Steinhaus concerning binary sequences ( and ), Technical report, LMPA, .
28. Optimally Small Sumsets in Finite Abelian Groups (, and ), Technical report, LMPA, .
29. A Survey on Modular Hadamard Matrices ( and ), Technical report, LMPA, .
30. Infinite families of links with trivial Jones polynomial (, and ), Technical report, LMPA, .
31. Circulant 16-modular Hadamard matrices and Jacobi sums ( and ), Technical report, LMPA, .
32. Three moves on signed surface triangulations (, and ), Technical report, LMPA, .
33. Circulant Modular Hadamard Matrices ( and ), Technical report, LMPA, .
34. Modular sequences and modular Hadamard matrices ( and ), Technical report, LMPA, .
35. The second Betti number of an edge ideal ( and ), Technical report, LMPA, .
36. On systems of binomials in the ideal of a toric variety ( and ), Technical report, LMPA, .
37. Restricted sumsets in finite vector spaces : The case $p=3.$ ( and ), Technical report, LMPA, .
38. Signed diagonal flips and the four color theorem (), Technical report, LMPA, .
39. Restricted sums of sets of cardinality $1+p$ in a vector space over Fp ( and ), Technical report, LMPA, .

février 2018 :