Inspired by work of McKay, Morse, and Wilf, we give an exact count of the involutions in Sn which contain a given permutation τ ∈ Sk as a subsequence; this number depends on the patterns of the first j values of τ for 1 ≤ j ≤ k. We then use this to define a partition of Sk, analogous to Wilf-classes in the study of pattern avoidance, and examine properties of this equivalence. In the process, w...

Let the sign of a standard Young tableau be the sign of the permutation you get by reading it row by row from left to right, like a book. A conjecture by Richard Stanley says that the sum of the signs of all SYTs with n squares is 2. We present a stronger theorem with a purely combinatorial proof using the Robinson-Schensted correspondence and a new concept called chess tableaux. We also prove ...

Motivated by Stanley's results in [7], we generalize the rank of a partition λ to the rank of a shifted partition S(λ). We show that the number of bars required in a minimal bar tableau of S(λ) is max(o, e + (ℓ(λ) mod 2)), where o and e are the number of odd and even rows of λ. As a consequence we show that the irreducible projective characters of S n vanish on certain conjugacy classes. Anothe...

In this note, we describe various theoretical results, numerical computations, and speculations concerning the analytic properties of the Shintani zeta functions associated to the space of binary cubic forms. We describe how these zeta functions almost fit into the general analytic theory of zeta and L-functions, and we discuss the relationship between this analytic theory and counting problems...

In recent years a great number of advanced theoretical - empirical methods has been developed for design & modeling concrete pavements distress. But there is no reliable theoretical method to be use in evaluation of conerete pavements distresses and making a decision about repairing them. Only empirical methods is used for this reason. One of the most usual methods in evaluating concrete paveme...

At the heart of Kunitz, Markee, and Sert’s (2021) edited volume is question how classroom interaction can contribute to second language acquisition. Using conversation analysis (CA) as a methodological tool answer this question, editors contributing authors book also endeavor package their findings in ways that are accessible for all kinds teaching professionals (e.g., pre- in-service teachers,...

A texturing method for the semi-analytic polygon computer-generated hologram synthesis algorithm is studied. Through this, the full-potential and development direction of the semi-analytic polygon computer-generated holograms are discussed and compared to that of the conventional numerical algorithm of polygon computer-generated hologram generation based on the fast Fourier transform and biline...