A t-intersecting constant dimension subspace code C is a set of k-dimensional subspaces in projective space \(\mathrm {PG}(n,q)\), where distinct intersect exactly t-dimensional subspace. classical example such the sunflower, all pass through same t-space. The sunflower bound states that if \(|C| > \left( \frac{q^{k + 1} - q^{t 1}}{q \right) ^2 1\). In this article we will look at case \(t=0\) ...

Let q be a prime power and k ≥ 2 be an integer. In [2] and [3] it was determined that the number of components of certain graphs D(k, q) introduced in [1] is at least qt−1 where t = b k+2 4 c. This implied that these components (most often) provide the best-known asymptotic lower bound for the greatest number of edges in graphs of their order and girth. In [4], it was shown that the number of c...

The Delannoy numberD(h,k)=∑j=0h(kj)(h+k−jk) counts all lattice paths from (0,0) to (h,k) by using the steps (1,0), (0,1) and (1,1). Define q-Delannoy numberDq(h,k)=∑j=0hq(j+12)[kj]q[h+k−jk]q. Using a combinatorial interpretation of Dq(h,k) based on area statistics, we prove Lucas-type congruence for numbers.

Suppose M is a closed irreducible orientable 3-manifold, K is a knot in M , P and Q are bridge surfaces for K and K is not removable with respect to Q. We show that either Q is equivalent to P or d(K,P ) ≤ 2 − χ(Q − K). If K is not a 2-bridge knot, then the result holds even if K is removable with respect to Q. As a corollary we show that if a knot in S has high distance with respect to some br...

The bivariate big q-Jacobi polynomials are defined by [3] Pn,k(x, y; a, b, c, d; q) := Pn−k(y; a, bcq , dq; q) y(dq/y; q)k Pk (x/y; c, b, d/y; q) (n ≥ 0; k = 0, 1, . . . , n), where q ∈ (0, 1), 0 < aq, bq, cq < 1, d < 0, and Pm(t;α, β, γ; q) are univariate big q-Jacobi polynomials, Pm(t;α, β, γ; q) := 3φ2 ( q−m, αβq, t αq, γq ∣∣∣∣ q; q) (m ≥ 0) (see, e.g., [1, Section 7.3]). We give structure r...

A matroid is uniform if and only it has no minor isomorphic to U1,1?U0,1 paving U2,2?U0,1. This paper considers, more generally, when a M Uk,k?U0,?-minor for fixed pair of positive integers (k,?). Calling such (k,?)-uniform, shown that this equivalent the condition every rank-(r(M)?k) flat nullity less than ?. Generalising result Rajpal, we prove any (k,?) prime power q, finitely many simple co...

Let d(n; q) be the number of labeled graphs with n vertices, q N = ? n 2 edges, and no isolated vertices. Let x = q=n and k = 2q ?n. We determine functions w k 1, a(x), and '(x) such that d(n; q) w k ? N q e n'(x)+a(x) uniformly for all n and q > n=2.

We will define the extension of q-Hurwitz zeta function due to Kim and Rim (2000) and study its properties. Finally, we lead to a useful new integral representation for the q-zeta function. 1. Introduction. Let 0 < q < 1 and for any positive integer k, define its q-analogue [k] q = (1 − q k)/(1 − q). Let C be the field of complex numbers. The q-zeta function due

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