Adopting the definition of excedances of type B due to Brenti, we give a type B analogue of the q-derangement polynomials. The connection between q-derangement polynomials and Eulerian polynomials naturally extends to the type B case. Based on this relation, we derive some basic properties of the q-derangement polynomials of type B, including the generating function formula, the Sturm sequence ...

A familyB of sequences has the Ramsey property if for every positive integer k, there exists a least positive integer fB(k) such that for every 2-coloring of f1;2; : : : ; fB(k)g there is a monochromatic k-term member of B. For fixed integers m > 1 and 0 q < m, let Bq(m) be the collection of those increasing sequences of positive integers fx1; : : : ;xkg such that xi+1 xi q(mod m) for 1 i k 1. ...

An N-dimensional real representation E of a finite group G is said to have the “Borsuk-Ulam Property” if any continuous G-map from the (N + 1)-fold join of G (an N-complex equipped with the diagonal G-action) to E has a zero. This happens iff the “Van Kampen characteristic class” of E is nonzero, so using standard computations one can explicitly characterize representations having the B-U prope...

A first-order theory T has the Independence Property provided T ⊢ (Q)(Φ ⇒ Φ1 ∨ · · · ∨ Φn) implies T ⊢ (Q)(Φ ⇒ Φi) for some i whenever Φ,Φ1, . . . ,Φn are formulae of a suitable type and (Q) is any quantifier sequence. Variants of this property have been noticed for some time in logic programming and in linear programming. We show that a first order theory has the independence property for the ...

Let Q-L be the least predicate extension of a normal extension L of S4 and BF be the Barcan formula ∀x2A(x) ⊃ 2∀xA(x). Ghilardi [3] showed that it is rare that Q-L is complete with respect to Kripke semantics. On the other hand, if L is a subframe logic with the finite embedding property, we can show the completeness of Q-L + BF by the method of canonical models (cf. Lemma 3 [2], Theorem 3.9 [5...

A retraction from a structure P to its substructure Q is a homomorphism from P onto Q that is the identity on Q. We present an algebraic condition which completely characterises all posets and all reflexive graphs Q with the following property: the class of all posets or reflexive graphs, respectively, that admit a retraction onto Q is first-order definable.

A set A ! is computably enumerable (c.e.), also called recursively enumerable, (r.e.), or simply enumerable, if there is a computable algorithm to list its members. Let E denote the structure of the c.e. sets under inclusion. Starting with Post 1944] there has been much interest in relating the deenable (especially E-deenable) properties of a c.e. set A to its information contentt, namely its T...

Two well-known q-Hermite polynomials are the continuous and discrete q-Hermite polynomials. In this paper we consider a new family of q-Hermite polynomials and prove several curious properties about these polynomials. One striking property is the connection with q-Fibonacci and q-Lucas polynomials. The latter relation yields a generalization of the Touchard-Riordan formula.

An additive and hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphism. Let P and Q be two additive and hereditary graph properties and let r, s be integers such that r ≥ s. Then an r s -fractional (P,Q)-total coloring of a finite graphG = (V,E) is a mapping f , which assigns an s-element subset of the set {1, 2, . . . , r} to each vert...

There is a type of distance-regular graph, said to be $Q$-polynomial. In this paper we investigate generalized $Q$-polynomial property involving graph that not necessarily distance-regular. We give detailed description an example associated with the projective geometry $L_N(q)$.