Zobrazeno 1 - 10
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pro vyhledávání: '"Tom, Foster"'
Autor:
Tom, Foster
We prove that a tree with a vertex of degree at least five must be missing a connected partition of some type and therefore its chromatic symmetric function cannot be $e$-positive. We prove that this also holds for a tree with a vertex of degree four
Externí odkaz:
http://arxiv.org/abs/2409.12934
Autor:
Sagan, Bruce E., Tom, Foster
We prove necessary conditions for certain elementary symmetric functions, $e_\lambda$, to appear with nonzero coefficient in Stanley's chromatic symmetric function as well as in the generalization considered by Shareshian and Wachs. We do this by fir
Externí odkaz:
http://arxiv.org/abs/2407.06155
Autor:
Tom, Foster
We prove a new signed elementary symmetric function expansion of the chromatic quasisymmetric function of any natural unit interval graph. We then use a sign-reversing involution to prove a new combinatorial formula for K-chains, which are graphs for
Externí odkaz:
http://arxiv.org/abs/2311.08020
Autor:
Tom, Foster
We prove that two horizontal-strip LLT polynomials are equal if the associated weighted graphs defined by the author in a previous paper are isomorphic. This provides a sufficient condition for equality of horizontal-strip LLT polynomials and yields
Externí odkaz:
http://arxiv.org/abs/2110.07984
Autor:
Tom, Foster
In recent years, Alexandersson and others proved combinatorial formulas for the Schur function expansion of the horizontal-strip LLT polynomial $G_\lambda(x;q)$ in some special cases. We associate a weighted graph $\Pi$ to $\lambda$ and we use it to
Externí odkaz:
http://arxiv.org/abs/2011.13671
Autor:
Tom, Foster
Publikováno v:
European J. of Combin. 90 (2020)
We consider the problem of determining when the difference of two ribbon Schur functions is a single Schur function. We fully classify the five infinite families of pairs of ribbon Schur functions whose difference is a single Schur function with corr
Externí odkaz:
http://arxiv.org/abs/1810.00533
Publikováno v:
Electron. J. Combin. 25 50pp (2018)
McNamara and Pylyavskyy conjectured precisely which connected skew shapes are maximal in the Schur-positivity order, which says that $B\leq _s A$ if $s_A-s_B$ is Schur-positive. Towards this, McNamara and van Willigenburg proved that it suffices to s
Externí odkaz:
http://arxiv.org/abs/1711.10000
We prove two related concentration inequalities concerning the number of rational points of hyperelliptic curves over subsets of a finite field. In particular, we investigate the probability of a large discrepancy between the numbers of quadratic res
Externí odkaz:
http://arxiv.org/abs/1710.02781
Autor:
Tom, Foster
Publikováno v:
In European Journal of Combinatorics December 2020 90
Autor:
Tom Foster, Simon Warwick
Publikováno v:
Research in Learning Technology, Vol 26, Iss 0, Pp 1-14 (2018)
There is growing evidence that incorporating games into education supports active learning and student participation. With that in mind, we created a staff development session that involved a playful learning activity, in which attendees experienced
Externí odkaz:
https://doaj.org/article/f5c1fce0ad844d6ba4aeabc77fed1956