# לוח אירועים כללי

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2018
אירועים בתאריך 17 באפריל 2018

## סמינר המחלקה למתמטיקה

תאריך:17.4.2018
שעה:00:00
מיקום: EM303
זמן תחילת האירוע: 13:00
זמן סיום האירוע: 14:00
הגוף המארגן: המחלקה למתמטיקה
קהל יעד: פתוח לכולם
תיאור האירוע: Speaker: Dr. Ofir Schnabel, Haifa University Title: How we can partition the integers into arithmetic progressions and related questions Abstract The evens and odds form a partition of the integers into arithmetic progressions. It is natural to try to describe in general how the integers can be partitioned into arithmetic progressions. For example, a classic result from the 1950's shows that if a set of arithmetic progressions partitions the integers, there must be two arithmetic progressions with the same difference. Another direction is to try to determine when such a partition is a proper refinements of another non-trivial partition. In my talk I will give some of the more interesting results on this subject, report some (relatively) new results and present two generalizations of partitioning the integers by arithmetic progressions, namely: 1. Partitions of the integers by Beatty sequences (will be defined). 2. Coset partition of a group. The main conjecture in the first topic is due to A. Fraenkel and describes all the partitions having distinct moduli. The main conjecture in the second topic, due to M. Herzog and J. Schonheim, claims that in every coset partition of a group there must be two cosets of the same index. Again, we will briefly discuss the history of these conjectures, recall some of the main results and
שם איש קשר: פרופ' חגי כתריאל
דוא"ל: katriel@braude.ac.il