Speaker: Ferdinand Ihringer

Title:  The Erdős-Matching Conjecture, Low Degree Boolean Functions and Their q-Analogs

Date/Time:  27 October 2021 / 13:40 - 14:30 PM

Zoom: Meeting ID:https://sabanciuniv.zoom.us/j/97158103830?pwd=dUpzMVYvcE9GUUJkSHVId1BwUlpxQT09

Passcode: 658402

Abstract: The Erdős-Matching Conjecture asks for the size of the largest family of k-sets of {1,…,n} without s+1 are pairwise disjoint members. Here we will discuss the equivalent problem for k-spaces in the n-dimensional vector space over the eld with q elements in the context of the classification problem of (almost) low degree families.

The talk will be based on results in [1, 2, 3, 4].

References
[1] J. De Beule, J. D'haeseleer, J. Mannaert, F. Ihringer, Degree 2 Boolean Functions on Grassmann Graphs, in preperation.

[2] Y. Filmus and F. Ihringer, Boolean degree 1 functions on some classical association schemes, J. Combin. Theory Ser. A 162 (2019) 241-270.

[3] Y. Filmus and F. Ihringer, Boolean constant degree functions on the slice are juntas,Discrete Math. 342(12) (2019) 111614.

[4] F. Ihringer, Remarks on the Erds Matching Conjecture for vector spaces, European J.Combin. 94 (2021) 103306.