WebSep 30, 2024 · We study the statistics area, bounce and dinv associated to polyominoes in a rectangular box m times n. We show that the bi-statistics (area, bounce) and (area, dinv) … WebThe q −Narayana numbers are polynomials in q with integer coefficients. The first values of these q −Narayana numbers are given in the following table: 1 q1 q3 2q+q2 1 q6 q2 +2q3 …
Rigged Configurations and Catalan, Stretched Parabolic Kostka Numbers …
WebVolume 218, Issue 12, 15 February 2012, Pages 6661-6665. Touchard like polynomials and generalized Stirling numbers. Author links open overlay panel G. Dattoli a, B. Germano b, … WebON TOUCHARD’S CONTINUED FRACTION AND EXTENSIONS: COMBINATORICS ... We did not go for an exhaustive list of continued fractions of the Touchard type, in order to keep this paper short and crisp. However, we are ... Our goal will be achieved once we are able to establish the identity B(q) = B(1) X k≥0 (−1)kq(k+1 2)vk. TOUCHARD’S CONTINUED ... piggly wiggly bush la weekly ad
Touchard type identity for q-Narayana numbers - ResearchGate
WebMar 13, 2024 · The behavior of a program that adds specializations for type_identity is undefined. Contents. 1 Member types; 2 Helper types; 3 Possible implementation; 4 Notes; 5 Example Member types. Name Definition type: T Helper types. template < class T > using type_identity_t = typename type_identity < T >:: type; Webdefine the type Bq-Eulerian number EB n,k(q) as follows: EB n,k(q) = X π∈Bn ⌊fwex(π)/2⌋=k qcr(π). Theorem 2.1. For any 0 ≤ k≤ n, we have EB n,k(−1) = n k, EB n,k(0) = n k 2 (the Narayana numbers of type B), En,k(1) is the type BEulerian number, and (4) EB n,k(q) = EB n,n−k(q). In Section 5 we consider crossings and alignments ... WebAbstract. We prove a conjecture of Liu and Wang on the q-log-convexity of the Narayana polynomials of type B. By using Pieri's rule and the Jacobi-Trudi identity for Schur … piggly wiggly broad st sumter