Showing papers in "Journal of Combinatorial Theory, Series A in 2005"

TL;DR: It is proved that, for every family F of n semi-algebraic sets in Rd of constant description complexity, there exist a positive constant e that depends on the maximum complexity of the elements of F, and two subfamilies F1, F2 ⊆ F with at least en elements each.

TL;DR: It is shown that if a family of lattice congruences On the symmetric groups satisfies certain compatibility conditions then the family defines a sub Hopf algebra of the Malvenuto-Reutenauer Hopfgebra of permutations, which is described by a type of pattern avoidance.

TL;DR: A model of particles jumping on a row of cells, called in physics the one-dimensional totally asymmetric exclusion process (TASEP), is considered and a combinatorial interpretation and a simple proof of these observations are given.

TL;DR: It is shown that the sphere is flag whenever the poset P has width at most 2, and it is speculated that the proper context in which to view both of these conjectures may be the theory of Koszul algebras, and some evidence is presented.

TL;DR: The result is gerneralized to a larger class of simplicial complexes including some of the complexes appearing in the work of Herzog and Trung on determinantal ideals and demonstrated that the number of such maximal sets in is counted by a k × k determinant of Catalan numbers.

TL;DR: The conjecturally positive k-Schur expansion coefficients for Macdonald polynomials could be described by a q, t-statistic on these tableaux, or equivalently on reduced words for affine permutations, as suggested by the conjectured k-Pieri rule.

TL;DR: The order of magnitude of ex(n, P) for all patterns P with four 1 entries is found and certain collections of excluded patterns often yield interesting extremal functions different from the functions obtained from any one of the patterns considered.

TL;DR: A combinatorial proof of Harer and Zagier's formula for the disjoint cycle distribution of a long cycle multiplied by an involution with no fixed points, in the symmetric group on a set of even cardinality is given.

TL;DR: First it is shown what conditions are necessary for a symmetric design to admit an imprimitive, flag-transitive automorphism group, and it is proved that for λ ≤ 3, the group must be affine or almost simple.

TL;DR: A family of bijective maps is constructed between the set PG of G-parking functions and the set JG of spanning trees of G rooted at 0, thus providing a combinatorial proof of |PG| = |JG|.

TL;DR: For an element w in the Weyl algebra generated by D and U with relation DU = UD + 1, the normally ordered form is w = Σci,j Ui Dj as discussed by the authors.

TL;DR: In this paper, the maximum size of a family of subsets of an n-element set not containing four distinct members was shown to be equal to the sum of the two largest binomial coefficients of order n.

TL;DR: In this paper, simplicial trees are studied as higher-dimensional graphs in order to produce algebraic statements about their facet ideals, and a large class of square-free monomial ideals with Cohen-Macaulay quotients are introduced.

TL;DR: In this paper, it was shown that the polynomial (bx + a)f(x) + (dx + c)g(x), whose leading coefficients have the same sign, is a PF sequence.

TL;DR: A very short proof of a result by Fraenkel and Simpson which states that the number of distinct squares in a word of lengh n is at most 2n is given.

TL;DR: It is shown that σ (Sn) ≤ 2n-1, while for alternating groups the authors find σ(An) ≥ 2 n-2 unless n = 7 or 9, and exact or asymptotic formulas are given for ρ(Sn).

TL;DR: It is shown that for any D, there is a 2-dimensional triangle P such that D(P) = D but such that the minimum period of ip(n) is 1, that is, ip( n) is a polynomial in n.

TL;DR: A new proof of the existence of an LSTS(v) for any v ≡ 1 or 3 (mod 6) with six possible exceptions and a definite exception v = 7 is given.

TL;DR: This work examines a related combinatorial model called groves, created by Carroll and Speyer as combinatorsial interpretations for Laurent polynomials given by the cube recurrence, which has observable frozen regions which it describes precisely via asymptotic analysis of a generating function.

TL;DR: It is proved that any 2-factorization of the complete graph admitting G as a sharply vertex transitive automorphism group is equivalent to a suitable 2-starter in G.

TL;DR: In this paper, the authors studied the distribution of the component spectrum of combinatorial structures such as uniform random forests, in which the classical generating function for the numbers of (irreducible) elements of the different sizes converges at the radius of convergence; this property is expressed in terms of the expectations of independent random variables Zj, j ≥ 1, whose joint distribution, conditional on the event that Σnj=1 jZj = n, gives the distribution for a random structure of size n.

TL;DR: In this article, a new approach to the enumeration of words on at most k letters of length n avoiding a given pattern was proposed, based on an automaton which for fixed k generates the words that avoid a given permutation pattern.

TL;DR: A new proof of Stanley's multivariate version of the Aztec diamond theorem is obtained and a combinatorial identity on the number of plane partitions is also given.

TL;DR: In this paper, a constructive proof of Fan's combinatorial lemma on triangulated spheres is presented, which differs from earlier proofs in the sense that it is constructive for a more general class of triangulations than the usual version.

TL;DR: In this paper, a product formula for the generating function of major index over the symmetric group was given, and several extensions are given in this paper, including a recurrence formula, a specialization at roots of unity and type B analogues.

TL;DR: In this paper, the first known example for a pattern q for which L(q)=limn-∞ √Sn(q) is not an integer was given, where Sn denotes the number of permutations of length n avoiding the pattern q.

TL;DR: It turns out that, in spite of great variety of approaches and definitions, all Z 2-graph complexes associated to G can be viewed as avatars of the same object, as long as their Z2-homotopy types are concerned.

TL;DR: A strengthening of the classical Chung-Feller theorem and a weighted version for Schroder paths are proved by refined bijections which are developed from the study of Taylor expansions of generating functions.

TL;DR: This paper describes precisely the class of partial words w with one hole for which the weak period is locally detectable in at least one position of w and provides an algorithm which computes a critical factorization when one exists.

TL;DR: It is shown that a valuation of a finite thick dual polar space is the extension of an SDPS-valuation if and only if no induced hex valuation is ovoidal or semi-classical.