We consider the following q-analog of the basic combinatorial search problem: let q be a prime power and GF(q) the finite field of q elements. Let V denote an n-dimensional vector space over GF(q) and let v be an unknown 1-dimensional subspace of V . We will be interested in determining the minimum number of queries that is needed to find v provided all queries are subspaces of V and the answer...

Egecioglu, ii. and J.B. Remmel, Brick tabloids and the connection matrices between bases of symmetric functions, Discrete Applied Mathematics 34 (1991) 107-120. Let H, denote the space of symmetric functions, homogeneous of degree n. In this paper we introduce a new set of combinatorial objects called I-brick tabloids and its variants, which we use *to give combinatorial interpretations of the ...

The Birkhoff polytope Bn is the convex hull of all (n×n) permutation matrices, i.e., matrices where precisely one entry in each row and column is one, and zeros at all other places. This is a widely studied polytope with various applications throughout mathematics. In this paper we study combinatorial types L of faces of a Birkhoff polytope. The Birkhoff dimension bd(L) of L is the smallest n s...

Combinatorial design theory traces its origins to statistical theory of experimental design but also to recreational mathematics of the 19th century and to geometry. In the past forty years combinatorial design theory has developed into a vibrant branch of combinatorics with its own aims, methods and problems. It has found substantial applications in other branches of combinatorics, in graph th...

a compact formulation of the set of tours neither in a graph nor its complement is presented and illustrates a general methodology proposed for constructing polyhedral models of decision problems based upon permutations, projection and lifting techniques. directed hamilton tours on n vertex graphs are interpreted as (n-1)- permutations. sets of extrema of birkhoff polyhedra are mapped to tours ...

In 1979 Kazhdan and Lusztig defined, for every Coxeter group W , a family of polynomials, indexed by pairs of elements ofW , which have become known as the Kazhdan-Lusztig polynomials of W , and which have proven to be of importance in several areas of mathematics. In this paper we show that the combinatorial concept of a special matching plays a fundamental role in the computation of these pol...

The study of the combinatorial properties of strings of symbols from a finite alphabet (also referred to as words) is profoundly connected to numerous fields such as biology, computer science, mathematics, and physics. In this paper, we examine to which extent some fundamental combinatorial properties of words, such as conjugacy, remain true for partial words. The motivation behind the notion o...

In a previous paper ([10]) the second author showed that if M is a pseudomanifold with complementarity other than the 6-vertex real projective plane and the 9-vertex complex projective plane, then M must have dimension ≥ 6, and in case of equality M must have exactly 12 vertices. In this paper we prove that such a 6-dimensional pseudomanifold does not exist. On the way to proving our main resul...

For a Specht module S for the symmetric group Σd, the cohomology H (Σd,S ) is known only in degree i = 0. We give a combinatorial criterion equivalent to the nonvanishing of the degree i = 1 cohomology, valid in odd characteristic. Our condition generalizes James’ solution in degree zero. We apply this combinatorial description to give some computations of Specht module cohomology, together wit...