Egge and Mansour have recently studied permutations which avoid 1243 and 2143 regarding the occurrence of certain additional patterns. Some of the open questions related to their work can easily be answered by using permutation diagrams. As for 132-avoiding permutations the diagram approach gives insights into the structure of {1243, 2143}-avoiding permutations that yield simple proofs for some...

We provide a 3/2-approximation algorithm for an offline budgeted allocations problem with applications to sponsored search auctions. This an improvement over the e/(e−1) approximation of Andelman and Mansour [1] and the e/(e − 1) − approximation (for ≈ 0.0001) of Feige and Vondrak [2] for the more general Maximum Submodular Welfare (SMW) problem. For a special case of our problem, we improve th...

For an arbitrary ribbon graph G, the partial-dual Euler-genus polynomial of G is a generating function that enumerates partial duals by Euler genus. When orientable graph, genus Gross, Mansour, and Tucker inaugurated these distribution problems in 2020. A bouquet one-vertex graph. Given its same as some bouquet; this motivates our focus on bouquets. We obtain polynomials for all bouquets with a...

0; n < m for n and m non-negative integers. Binomial coefficients play an important role in many areas of mathematics, including number theory, statistics and probability. Reciprocal binomial coefficients are also prolific in the mathematical literature and many results on reciprocals of binomial coefficient identities may be seen in the papers of Mansour [1], Pla [2], Rockett [3], Sury [5], Su...

The sponge construction, designed by Bertoni, Daemen, Peeters, and Ass­ cheis, is the framework for hash functions such as Keccak, PHOTON, Quark, and spon­ gent. The designers give a keyed sponge construction by prepending the message with key and prove a bound on its pseudorandomness in the ideal permutation model . In this paper we give a different keyed sponge construction that is based on t...

1. Nogová L, Reineke T, Brillant C, et al; German Hodgkin Study Group. Lymphocytepredominant and classical Hodgkin’s lymphoma: a comprehensive analysis from the German Hodgkin Study Group. J Clin Oncol. 2008;26(3):434-439. 2. Savage KJ, Skinnider B, Al-Mansour M, Sehn LH, Gascoyne RD, Connors JM. Treating limited-stage nodular lymphocyte predominant Hodgkin lymphoma similarly to classical Hodgk...

Integral Hamzeh Agahi,1,† Adel Mohammadpour,1,∗ Radko Mesiar,2,3,‡ S. Mansour Vaezpour1,§ Department of Statistics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran 15914, Iran Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, SK-81368 Bratislava, Slovakia Institute of In...

The simplicity and widespread use of blockciphers based on the iterated Even–Mansour (EM) construction has sparked recent interest in the theoretical study of their security. Previous work has established their strong pseudorandom permutation and indifferentiability properties, with some matching lower bounds presented to demonstrate tightness. In this work we initiate the study of the EM ciphe...

The iterated Even-Mansour (EM) scheme is a generalization of the original 1-round construction proposed in 1991, and can use one key, two keys, or completely independent keys. In this paper, we methodically analyze the security of all the possible iterated Even-Mansour schemes with two n-bit keys and up to four rounds, and show that none of them provides more than n-bit security. In particular,...